I run the Eggbeater MTB pedals on the front and my wife has Shimano SPDs on the back. It works for us as I have Eggbeaters on my MTB and she runs SPD's on her single.
FWIW, I did run the Eggbeaters for a little while on my single but switched back to Ultegra SPD-SL's because I thought the Eggbeaters were a little squirelly when sprinting.
I agree with the above posters about preferring MTB shoes (and pedals) on the Tandem. For me it provides a more solid footing at stops.
Duane