Hi Jessica!
Welcome to the Disney Parks Moms Panel! I've visited Walt Disney World Resort with my almost-three-year-old four times. A month ago I joined my three best mom friends with our collective five kids (all who were under age three) but one trip it was just my son and I. You're right, waking a sleeping Disney Baby for any reason can be not so magical.
Table Service restaurants have a No Stroller policy as the aisles need to remain clear for the safety of the servers and the other guests. Some dining locations like Whispering Canyon have really fun antics. Others like Crystal Palace and Ohana will invite children to participate in an 'around the restaurant' parade with their favorite characters. Luckily, all Table Service restaurants do have Stroller Parking nearby. And you're more than welcome to bring in items like high chair covers or a baby wearing carrier to make meal time easier.
Should your Mouseketeer fall asleep right before a scheduled meal you can certainly ask if he can remain in the stroller and be seated in an off-to-the-side area; however, there are no guarantees that the request can be accommodated, and done so in the same time frame as the reservation. If someone did need to stay behind with the sleeping babe while the rest of the group kept the reservation, that one-less guest would not incur a cancelation fee.
My family tries our best to not schedule meals that need reservations anywhere near nap time, so we usually book breakfasts and dinners only, leaving lunch open to find something yummy that we see (or smell!) as we pass by. And on the friend trip with all of the kids, we ended up in our Disney Resort Hotel's Quick-Service option almost every night for dinner, but there were so many menu choices that none of us ever felt tired of the selection.
I hope this helped, Jessica, and We'll See You Real Soon!
~Kristen