You can actually do this solo using a 2nd account on your console that you're friends with. You don't have to play live, so you can switch between the profiles to take your turn.
Setup the game and invite your 'friend'. Go back to main menu and press Y to switch profiles.
The online game should be there waiting for you in the online saved game list. If not, try setting up the game with the other profile.
A quick win is using these moves:
2: D8-H4 Checkmate
Player 1 loses, so you may need to adjust if your main is going first.
Just exit back to main menu after each turn. You'll probably be getting Xbox messages saying it's each profile's move.
This only works if you can connect to the damn server. i can't help with that bit.