Not experienced with poly, weddings, but might this help?
1) What's your budget? The traditional wedding isn't wallet friendly. Figure out what is reasonable to spend first, and then work around that.
2) What parts of a wedding matters most to everyone? Get from everyone a list of must-haves before deciding on style. For instance, someone might want to get their hair done all nice at a salon, which needs to be budgeted and accounted for in the overall tone of the wedding. If no one particularly cares for booze, that could go out the window to make room for more desired things. This might work a long way on compromise.
3) Is confirming that this is a relationship the only reason for a traditional wedding? It might be more beneficial to have the reception be causal and the ceremony be formal to get the best of both worlds(Or the opposite, I suppose). But consider making arrangements for time to change, a place to change, and possible travel between the two areas if there are two areas. Also make sure to know how to tell everyone clearly the plan for such if done.
4) Alternatively, figure out if any traditions come from one of the three sides that people want, or might help reinforce the idea of a stable, long term relationship. Something more personal might work then other traditions, unless you happen to be the sort of household to make new traditions.
5) Fancy up the invitations. If you need to reinforce what is going on, put it smack dab on the piece of paper and the save the date card.
6) Invite people from all three families. If they are confused, at least they can be confused together? Consider giving a reading to all three branches if possible.
7) I'd avoid having anyone stand up with you--People might get a little confused. In particular if you are wearing different styles of dresses to account for taste and different appearances. The exception MIGHT be the flower girl or the ring bearer--Some people (and the kids in question) really enjoy this and it's pretty easy to distinguish from the actual participants.