I think you play it the same way, with a few differences:
-Your goal is to get the most Duchies. This is usually your goal, but now it's even more true.
-Estates are no longer dead because they can turn into Duke, so you can buy Estates on $2/$3 turns more often. I think Silver > Estate if you already have some though.
- When Rebuilding, name Duchy, turn Estate->Duchy/Duke, Duke->Province, Province->Province
If you lost the Duchy split, odds are you just lose, since I don't think you can afford to trash Duchies->Province when your opponent has the option of either Duke or Province for VP. Think of it this way: whenever you Rebuild Duchy->Province you get +3 VP. If you have 4 Duchies, then Estate->Duke is also 3 VP, and buying some extra Estates to Rebuild along the way is a lot easier, while leaving you the option of Rebuilding to Provinces to force a game end.