I don't think it would make much difference, since the Epcot parking lot is a zoo for Princess as well. I think your best bet is to take the AK bus from Poly. It's not 100% foolproof, but parks buses generally have ways around the worst of the race congestion. You should really be OK.
The race starts at 5:00, and it goes to Magic Kingdom and back. Let's say the last corral starts at 6:00 AM and those people are doing a 16 minute per mile pace. When they leave Magic Kingdom and pass the Grand Floridian and Polynesian on the way back, they clear that area at about mile 8. So that's 128 minutes, so about two hours. That means the stragglers are out of your area by roughly 8:00.
Animal Kingdom opens for early entry at 7:30, right? So if you feel comfortable missing early entry and rope drop and head out after 8:00 you probably won't have delays. If you want to be there at 7:30, it might be a slower bus ride.
Might the bus get stuck in traffic? Yeah, maybe. But they usually do a really good job. I wouldn't give it a ton of worry.