Here's the deal....RAC (remote airline checkin) not DME is in charge of baggage checkin. The two are not tied together at all. So, calling and talking to Disney isn't going to get you anywhere.
Now...for the logistics. RAC opens at 5am. You have to be completely done with your transaction, bags checked and boarding passes in hand and walking away, no less than 3 hrs before flight departure. It takes about 15 mins (depending on any lines) to do this. IF your flight leaves at 7:55am, it is going to be completely, 100% impossible to meet the requirements of RAC. The earliest you could be done would be 5:15am....20 mins past the allowable time.
It really is no big deal to take your bags with you to the airport. Yes, it takes a bit longer since you now have to stop at the counter and check your bags. But, that's the way it's going to have to be.
For those wishing to use RAC with early morning flights, the earliest flight that is recommended is 8:30am. Anything before that is really chancy. You could run into longish lines and not be able to finish your transaction in the alloted time.