Bus to the MK and resort monorail or boat to the GF would be your best options using Disney transport. The boat dock is on the way to the monorail station from the bus depot, so unless there's a boat pulling out as you are walking by that may very well be quicker. The GF is the first stop the boat makes after leaving the MK, but it is the last stop before the monorail gets all the way back around to the MK.
DME will not pick you up at a resort other than the one where you are staying. The biggest challenge you have is that your pick up time will be approximately three hours before your flight time and you'll need to be back at BC and ready to go about 15 minutes before then. As a result, you probably want to plan on being back at BC by 10:30 a.m. Since I would leave at least an hour to get back using Disney transport, that would have you leaving 1900 PF at 9:30 a.m. You could stretch that to 10:00 a.m. or maybe 10:15 a.m. if you take a cab back to the BC from the GF.
Also, I would use RAC to check your bags at the resort and get your boarding passes. You can do that as soon as the desk opens at 5:00 a.m. and have to have it completed no later than 10:50 a.m. That will save you a little bit of fussing with luggage when you're ready to leave.
Bottom line is that your plan is doable only if you take a cab back to the BC after breakfast and that still doesn't leave you time for a true leisurely dining pace.