Domino Squad Nitpicks:

I assume the intro music transition is temporary, because there’s no fade, it just suddenly cuts in at 00:24.
I feel like the music could linger a little longer after the end of the cold open (3:32), or have the intro music come in sooner and harder. The gap feels odd and empty to me.
I’m not 100% sure the cold open is necessary; I think it’d work just as well to stick it after the intro text.
The “Echo” insertion works well. I wouldn’t suspect it if I hadn’t read the above discussion.
Is the music at 8:36 added? It overwhelms the dialogue.
The transition at 12:00 feels like it has the opposite problem to the one at 3:32, in that there’s no gap or pause whatsoever. We very rapidly leave the scene with Hevy and 99. I’d have been tempted to stick “TWO WEEKS LATER” on a black screen and linger for a moment, maybe even with a Majora’s Mask-esque musical queue, before fading back in.
In general, I’m not 100% sure about the idea of keeping two attempts. Maybe it’s just because I’m familiar with the original episode, but it feels like there’s a lot of unfinished business when we’re suddenly thrown ahead to Rookies. I think it’d be clearer if they just failed once, really hard, and then got sent to the listening station, because it gives less time for the audience to invest in the idea of them succeeding at that one specific test to prove Bric wrong. Fanediting is a complicated profession, though. (It’d also get us to Anakin/Obi-Wan’s plot sooner).
It is odd that Clone Cadets retconned half the clones in Rookies to be part of the same squad, because in Rookies they’re introduced with more “colleagues who have only recently met” vibes. Nothing you can do to fix this though, I don’t think.
Rookies plays out just fine, so if you did anything major to the content of this episode, it’s seamless and nothing is missed.
The lighting quality leap going into ARC Troopers is noticeable, but other than that, the transition is very cleanly executed. ~~(Clearly to solve this, you should personally recreate the entire of TCW Season 1.)~~ Echo and Fives painting their armour in 501st colours despite not being in the 501st yet is a little strange, but I agree that cutting the scene of them joining was the right choice, so it is what it is.
“Feels like yesterday we were here.” and the associated reminiscence is a little odd since it’s only been two weeks. Then again, it’s kind of a joke in the original episode as well, since they were just there in the previous release-order episode.
I’m not sure if you’ve done much to ARC Troopers, but I didn’t notice any issues.
The ending, with “in the 501st”, and the new music transition, works really well. The work that’s been put in on that, with McFibb and all, is paying off for sure.

All in all, your tweaks to the overall story work well, in my opinion. I think a little tweaking to the Clone Cadets segment might be worthwhile, and obviously Echo and Fives donning 501st armour prior to actually joining the 501st is a little odd, but it’s a smart edit that I think is stronger than the original episodes are by themselves.

If I had to complain, 50 minutes feels a little long to me - but that might just be because I’ve never cared that much for endless action scenes of clones and droids blasting one another (I’m more into the Jedi and Sith stuff), whereas I know some people who can’t get enough of the clone side of TCW.

Did 99 try to get those kids shot?