The "Desert Skip" can be used to skip multiple levels, and I believe which attract mode cutscene it plays first is essentially RNG (should be easy to manipulate). I believe I've gotten Abu's cutscene first while messing around with it with regular controller inputs.
If you time based on last input timing, the TAS can be a couple seconds long in this way:
https://youtu.be/35VFGRCYkjM
I timed the above method RTA and got 1 hour 48 min so obviously the "speed" of that trick is based purely on the timing system, not on any real time save.
However, assuming you can get Abu first by controlling when you do your input, I believe you can save a couple seconds by skipping 4 levels (Desert, Agrabah Rooftops, Sultan's Dungeon, and Cave of Wonders) and playing Flip's inputs for Agrabah Streets and from Escape -> end
There's also the possibility of using the skip selectively with soft resets, perhaps to skip Jafar's palace, although I'm skeptical.