I imagine that the Epcot line starts running an hour prior to park opening. If it's an EMH morning at Epcot, then the monorail should start by 7-7:30ish.
I wouldn't bother parking at Epcot and taking the monorail to the TTC. I would just drive to the TTC and either walk or monorail over to the Polynesian...it's a nice walk..takes under 10 mins.
Then, either drive over to Epcot, or take the monorail there.