Speaking of removing characters completely, I was thinking of an Anakinless (and possibly Tatooine-less) Episode I. In my ideal PT, the Prophecy would be entirely absent; and the focus wouldn’t be Anakin’s downfall, rather Palpatine’s rise. As such, it’s not really necessary to have Anakin at all in Episode I.

In a heavily re-worked Episode II, the introductory scene could be the speeder chase. The sequence could be turned into one unrelated to the main plot ala Indy’s intros, that would instead serve to establish Anakin and Obi-Wan as friends, and to start the movie with a bang.

Another possible intro for the character would be his frolicking with Padme in Naboo (minus the turd monsters), so their romance is already underway when the movie begins. I’m pretty sure most of their scenes together can be edited into an idyllic sequence, ideally they’re not in hiding. Padme would not be targeted, and Anakin would be on shore leave; before being called into action by the Council, which would not forbid love.