Thank you so much for your comments and a very thorough review, Zenslinger!
Now onto your questions:
When Mohaim is speaking to Jessica about the gom jabbar test, but before they enter Paul's room, at the very end of the scene, she says, "He is here." Referring, I assume, to Paul. I didn't rewatch the Theatrical Cut to prepare to make this post, but I don't remember this line from it. Why keep this? The line seems to have no purpose; it's obvious Paul is nearby.
The real reason that line exists in the first place is because the Mohiam scene was supposed to take place right before The Box scene. But it was switched to an earlier location. It makes a lot more sense in the original context, since Paul is approaching the door on foot.
I kept the order of scenes the same as the theatrical cut, because I didn't want to lose the beautiful dissolve from Jessica. The reason I didn't trim the extra line was because in terms of rythm, it gave the scene a better sense of closure, and one could also infer that Mohiam could sense Paul now because his dreaming was becoming more intense.
The scene, also in the Theatrical Cut, in which the Atreides soldiers intercept Harkonnen communications ("Battle language!") seems misplaced in your cut. It comes before the spice mining inspection and does not add, as it does in the TC, to the tension about the impending Harkonnen sneak attack.
The main reasons I kept this line was because it was a Theatrical scene (which I wanted to retain as much as possible), and because in the new context it can be inferred that it had to do with the Harkonnens intercepting the Carryall.
Another small scene that's in the TC, but is in a different spot here, is that of Yueh kneeling and crying. Here it comes after Yueh has sprung the trap, and has already been captured by the Harkonnens, but I don't think his hands are bound. In the TC it seems to be that he's crying about what he's going to do, but in Third Stage, it's because he's already done it. It doesn't seem to make sense, however, that he could get away from the Harkonnens long enough to have this moment alone.
This was included mostly to retain more Theatrical footage. It's difficult to determine exactly where this scene was supposed to be, because it's shifted to different locations in different scripts. So I decided to keep it where it was in the Theatrical version. The main problem with the Yueh subplot in the film is that a crucial bit of information is missing that isn't in any cut: Yueh believes his wife is being held hostage. Jessica's internal monologue of "They must have killed her," which was probably added for clarification (ironically), kind of muddies that implication. Since Yueh was under their control due to his wife, he probably could come and go as he pleased. But when he was fetched by Feyd, and later by the Baron, the Sardukar were probably ordered to keep him restrained while in the room with them. In that context I think the scene works where it is.
The scene between Jessica and the Shadout Mapes about the crysknife, for example, just doesn't play that well. From a fan's perspective, I'm glad to see it, but it would be a little difficult for someone who hadn't read the book several times to understand what's going on with the need for the crysknife to draw blood. Linda Hunt just doesn't make her lines completely clear.
Yes, there was supposed to be more internal monologue from Jessica. I'm paraphrasing here, but basically: After Shadout asks Jessica if she knows the meaning of the crysknife, Jessica internally thinks: "Crysknife means 'Maker of Death.'" So then Jessica says aloud "It's a Maker..." and Shadout screams, interrupting her. Jessica then internally thinks: "'Maker' is the key word. Sandworms are also called 'Makers' by the Fremen. The crysknife must be made of a Sandworm's tooth. That was close." So she retains the facade of being correct by saying aloud "Did you think I wouldn't know the Maker?"
Without Jessica's internal monologue (the scene was probably cut before post-production dubbing, since Shadout's eyes were not colored), the scene is a bit confusing. It's a little less confusing than the shorter version in the Extended Edition, though, IMO, where Shadout just drops to the floor for no particular reason! lol
Again, I really appreciate your comments! You also can thank Fanfiltration, whose fullscreen edit inspired many moments in this edit.