Seems to be a lot of incorrect info out there....so, there are early morning buses to the parks for the express purpose of getting guests from their resorts to those early breakfast ADRs and tours. The buses to the MK start about 6:30, sometimes a bit earlier.
You can take the MK bus, but be out at the stop by 6:15. When you get on the bus, ask the driver what the fastest way to the Polynesian is going to be. The driver may very well offer to drop you at the Polynesian after he goes to the MK.
The problem with ADRs before 7:30 is that the resort monorail doesn't start until 7:00 which makes it impossible to get to the Polynesian before that.
I guess the safest way is to take a cab. But, if the ADR were a bit later, I would have said to just go with the bus/monorail.