I don't think the current format is going to work out.
What if we made it all in spot #10?
An odd number of challenges so we can't have a tie.
Say aim for 7 games this time.
Since you guys won last season, you get 4 home games, we get 3 (odd games at home, even games on the road).
Do it like hs/college tennis -- our #1 vs. your #1, #2 v #2, and so on.
One captain from each conference submits teams numbered 1-7; if a team doesn't accept the challenge, we get a replacement from within that conference.
This should be much easier to get near full participation when it's just one game.