Several things you can do.
Option 1 (assuming everyone gives honest handicaps):
Seed palyers 1 thru 6. Have seeds 1, 4, 6 play match play agaisnt seeds 2, 3, 5. Seed 1v2 and seed 5 in one 3some and seed 3v4 and seed 6 in another 3some. Seeds 5 and 6 would have to card up after the round. You could adjust the scorecards prior to the round for match play. Meaning if Seed 1 is a 10 handicap and seed 2 is a 12 handicap then seed 2 gets a stroke on the 2 hardest holes. Make it your own little Ryder Cup format over 3 rounds. Theoretically any seed cold play any opponent.
Option 2 :
Play 3 somes agaisnt 3 some and make each 3some use at least 1-2 scores from each side or round to keep everyone involved. You caould also adjust the scorecard in this match. If you are worried about foot wedges split the teams up among the 3somes and compare cards after the round.
Have fun.