The boats usually start running about 1/2 hour before the parks open.
So unless there are Extra Magic Hours that morning the boat will probably not be running at 6:45-7:00.
You could take a cab (probably not that easy at 6:45) or you could ask a supervisor at Bell Services if someone could run you over in the Resort's van.
We got stuck at the Grand Floridian one night and that's what they did for us.
Either way I'd look into the night before.