I just started watching these (Thanks for the access) and am trying to take notes so that I can provide detailed feedback. What you have done is refreshing and makes this series much more watchable for me. Still, I think there are things that I would try to improve if I were the editor, and I’d like to provide my feedback in case you find any of it helpful.

Episodes 01x00 through 01x04:

01x00 - Dark Force Rising

While you did a good job with the material, I still find the differences in art style and characterization between this and the rest of the series distracting. It’s not bad by any means, but this episode is not going to be part of my normal rewatch, especially since 01x01 does such a good job of introducing the characters etc.

01x01 - The New Padawan

I love the intro with finding Maul, but there is no relevance for this in the episode, or in the next few episodes. Is this really the best place for that cold open?
Ventress talks with ObiWan as if she is an old girlfriend, but we get no context for that here. We also hear her talk about meeting them again, but outside of her mysterious fight with Anakin in episode 0, there is no known background for this ongoing interaction. She also mentions that ObiWan and the Republic were betrayed (as explanation for how the Separatists got there), but since that isn’t included in your series, is it really good to bring up? (Addendum: It becomes clear that Ventress talks with everyone as if she is an old girlfriend, but that’s not immediately clear in this encounter.)  Cutting all of the above dialogue may leave the fight too short, but is this scene even needed in this episode? You could start with ObiWan looking through the binoculars at the marching droids, or even with the battle in the street where Anakin jumps onto the turret droid. This would require rewriting the crawl to remove Ventress and dropping us directly into the action as Star Wars often does, with ObiWan and Anakin trying to help the people stationed on the planet hold off a Separatist army until reinforcements arrive.
It is confusing trying to figure out who is holding what position on or around the planet. There are droids everywhere and Ventress is there, but the Separatists land/invade at the end of the Ventress fight. There are Republic ships in orbit, and seemingly ObiWan and Anakin recently arrived, but then there are no Republic ships and communication has been cut off until the one Venator arrives with Asoka.  By removing the initial space scene with the bombers and the Ventress part with the Seperatists landing, the situation could be simplified. We would see a planet locked in kind of a stalemate, hear that communications have been blocked (ObiWan hasn’t been able to contact the admiral), and see that a single Venator has been ambushed trying to bring supplies and needs to get reinforcements. ObiWan says that their previous support ships (likely the ones that brought them there) were all destroyed at some prior point.
The initial scene with the admiral, Yoda, and Windu is unecessary. The same information is communicated by ObiWan, the crew of the Venator, and Yoda when Asoka arrives.
Bail Organa only appears in two small scenes (one at the beginning and one at the end). Neither communicates much other than the easter egg of his presence. Should he really be there at all, or does it all flow better without him?
I’ve watched several edits of the Prequel Trilogy and one of my favorite “improvements” is the removal of dialogue by the battle droids. The idea is that they are all networked and therefore only need to speak when communicating to other characters. It makes them less goofy and more threatening. I don’t know if you’d want to do a similar thing in your edits, but it may be worth considering. (Addendum: This could be much trickier in later episodes like The 501st.)
Not knowing the original version very well, I don’t know if anything worthy can be added. If all of the above is cut, it will likely take the current 28-minute episode down below 20 minutes. Is that too short, especially for what is essentially the opening of the series? I’m not sure. The episode does an excellent job of introducing Asoka, ObiWan, and Anakin, along with a lot of the Separatist droid models. It’s a much stronger opening than episode 0 or the vanilla episodes 1 and 2.

01x02 - The Death Watch

The number of quick shots in the opening strikes me as a bit overdone. We don’t need to see ObiWan in the cockpit, because we know it’s him from the crawl and from when he climbs out. I’m not sure we even need to see him undock from the hyperspace ring. The approach to the city is a nice introduction and reminds me of the opening to Attack of the Clones, but I could also imagine the episode starting with him landing and climbing out.
There’s probably nothing that you could do about it (the available footage is the available footage), but it seems very foolish for ObiWan to call the duchess to help him check out what he knows is a Death Watch hideout when he knows that they are after her.
Again, there’s probably not much you can do, but it would be nice if Anakin said something about where Asoka is when he shows up for escort duty. Maybe the crawl could be edited to reflect not only that he is taking her somewhere else, but specifically that he is dropping her off somewhere (maybe to visit family or something, if that makes sense in the context of the larger series).
The “stand by for lightspeed” mini-scene seems almost unnecessary and distracting from the scenes around it. I get that it shows why the view outside the windows changes, but I’m not sure it needs to be spelled out like that. You could replace it with the slightly-later establishing shot of the ship in hyperspace and remove that, making the Anakin ObiWan conversation a longer less-broken sequence.
This is a great episode. I have the impression that there was a lot more stuff with the assassin spiders in the lower decks - the way you handled them seemed just right to me. Everything in this episode blended well together. It had a steady pace and made me care about the characters and world.

01x03 - Malevolence

The crawl tells us about the big bad battleship Malevolence, but what if it was a mystery to the audience? It seems to be a mystery to the characters. They could know that Grievous is behind the mysterious attacks that are leaving behind no survivors.
I’m not sure about Grievous’ line about concern for troops being a weakness to exploit, because I’m not seeing how that’s being exploited at all in this episode, particularly in relation to the opening battle.
I’m not sure that the initial scene on the medical station is necessary. It confirms that the threat is a warship (reduces the mystery and suggests that they know for a fact that it is coming - how?). The danger to the station is logically deduced later by Anakin, so this scene might be able to be skipped without losing anything.
It seems to me that there are too many short scenes in the escape pod. Maybe the first one could be joined into the end of the opening battle to increase plot cohesion. Maybe this could happen right after Grievous says to destroy the escape pods.
The first scene with the Malevolent in hyperspace is probably not necessary. It also contributes to the idea that Grievous doesn’t know exactly what he and his ship are doing.
It’s strange that ObiWan contacts Anakin via holo after telling Yoda and Windu that he’s been in contact with Anakin. Is the ObiWan Anakin scene really needed? If cut, you would still have searching and the scene with Yoda and Windu, but the next time you cut to the shuttle, R2 would find the signal.
When Anakin is talking near the Y-Wings he surmises the next target of the Malevolent. That would then make sense as the setup for the evacuations. If you cut the initial scene on the station and move the second one, where they discuss evacuation progress to sometime soon after this scene, the plot will make more sense. Note that the transition from the Y-Wing conversation directly to the Malevolent in hyperspace is excellent - don’t change that. It will be even better if we lose that earlier shot of the ship in hyperspace.
Why does Grievous know that Skywalker is leading the fighters? Why does he care? I suggest trimming his battle lines/scenes to eliminate the Skywalker references.
Grievous says “impossible” twice, almost as if he doesn’t anticipate things going wrong ever. Since he clearly has an escape plan for himself, perhaps consider cutting the number of times he reacts with surprise to the battle going badly. Instead, keep him angry but deliberate in responding to the situation as it develops.

01x04 - The 501st Legion

While I really like most of your crawls, this one gives a lot of information that is later supplied contextually. It’s good to introduce the idea of the cloning facilities and Grievous being hunted, but the part about the trainees is hit pretty hard and explained thoroughly right after this. The sentence about Captain Rex supporting Anakin but also inspecting facilities is a bit strange. Maybe change it to something like “Meanwhile, CAPTAIN REX, who normally supports Anakin and the 501st Legion, has been given a special assignment to inspect the local clone outposts, in order to prepare them for possible Separatist attack.”
I’m not sure that you need as many scenes about the trainees at the beginning. They seem a bit repetitive, especially with the one bounty hunter/trainer trash-talking 99. At the same time, I’m not sure quite what to trim without losing too much.
Though not by your choice, there remains a lot of battle droid oddness in this episode. The droids communicate a lot with each other verbally and are unable to pick up on things going on around them, like when the clones are trying to pass for a droid at the door to the facility. It may not be possible to make the battle droids fully appear an efficient and lethal force, but you may wish to make adjustments that direction. Again, I’ve seen Prequel edits where they eliminate the droid chatter and imply that they are all networked - it helps.
When Ventress meets Anakin in the DNA room, we again get the feeling that it isn’t the first time. Most of their interaction can go either way, but his line “without saying hello” directly implies that they know each other. If we accept episode 0 and maintain her presence in episode 1, that works. If you skip 0 and remove her scene from 1, this line also needs to be trimmed.  I personally think that this episode can serve as a good introduction for Ventress. When she first appears, Grievous calls her “assassin,” and she says that she was given orders from Dooku. This is pretty much everything that has been established in her prior appearances (besides claiming to be a Sith). If this is the first time we see her, we learn what need to know, and she gets to do something integral to what is going on.
Why would Grievous know ObiWan by name? This again implies a prior interaction that was never shown. It wouldn’t be hard to trim that out of the scenes, making ObiWan (to Grievous) just some random Jedi that happens to be on Kamino. I like that the first time we see Grievous fight (if you don’t count episode 0) is vs ObiWan, who will eventually kill him in a rematch.