I'd keep all the basic lore, like lightsaber battles and the Jedi Council. I'd keep the no-attachments rule but deal with it more logically (shouldn't Padme be responsible enough that she'd take it seriously even if she didn't really understand it?)
I'd keep the Clone Wars, but have the clones be the cause of the war, not major combatants, and the bad guys would be the ones doing the cloning (to create slaves).
I'd even keep the Space Jesus notion for Anakin, but make the prophecy more vague and open to interpretation - he could save the Jedi or destroy them - and how people read it depends on what they want to read into it.
For instance, balancing the Force means equal power for Sith and Jedi. But the Jedi aren't going to like that idea, so they delude themselves that it means all power for the Jedi, none for the Sith. Meanwhile the Force gazes upon the mortal foolishness of Jedi and Sith alike with unconcerned equanimity. The Jedi may be good but they aren't wise.
Yeah, though it might be surprising to some, there really is quite a bit about the PT that is likable enough.
The most surprising thing for me in
TCW is how little actually needs to be changed to turn it into a kick-ass story! In some cases, just adding one background element (Separatists with reasonable motives) negates a huge problem (heroes look stupid for not being suspicious of a war with no reasonable cause).
Take the "theater" scene in ROTS between Palpatine and Anakin. It's a fantastic scene on its own merits.
With some vital changes to Anakin - he's likable and heroic but arrogant and stubborn; he has good reasons to mistrust democracy (the Republic is thoroughly corrupt, the audience sees evidence of thorough corruption and understands that he's never seen a healthy democracy, plus he loves power); and his love of power is drawing him already to the Dark Side (I'd like to see some scenes establishing he's checking out the Dark Side on his own initiative, nothing to do with Palps) - that scene would be terrific. So much of the PT was right, it rankles that a few vital mistakes sunk the whole thing.