Simple - may not be cheapest.

Simplest - take a cab (I took Disney's Magical Express once, and in my 20 visits to WDW it was the worst - over two hours from landing to the Boardwalk. Kids and I were so hot and tired and I almost left the line twice to go find a cab, but I didn't have enough cash on me and didn't remember that cabs take credit cards) TO Wilderness Lodge and book an extra night there. Easiest yes, but may not be as frugal.

Or, stay at the airport (I've stayed at the Renn there and it's nice with a shuttle, then next morning take a cab to WL to drop off luggage - very early I'd assume for your breakfast).

Or stay at the Hyatt in the airport.

If it were me, and you were my spouse, I'd also by the way kill you for making early breakfast ADR! I don't do breakfast and would hate to be checking into WL by at the very least 6:30am! That is no vacation to me!

My advice, is if you're going to make this early (UGH) reservation, just book another night at the WL.