It's a standard procedure that when the monorail is unable to run its standard schedule, they will add buses (and more shuttle boat capacity) to replace the monorail route(s.)
Not that this will actually help you (as I am just guessing,) but I figure the buses between the monorail resorts and TTC and MK should start around 7AM.
Hopefully someone on the ground at WDW can post firsthand observations.
The buses should start running between 7am - 7:15am. Plenty of time to get to meal reservations which start from 8am in the parks. If the park opens at 8am, the buses will start running from 7am