Maybe it's time to contact your NPC area advisor, and your panhellenic delegate(which I guess you've done).
From changes that are happening in NPC right now, you may find that you could have a less structured recruitment and still work together...
Of course I don't think it's fair the one group changing their vote, but they have the right to do so (if the issue is brought back up to council)
On my campus we also have just 2 NPC groups - we don't do formal recruitment. Neither of us wants to do it, and we are both more successful doing COB. We both do COB year round, usually after a period of informal recruitment in September.
My question, why is ABC so set on formal? Do they think they won't find as many interested women? And if XYZ isn't helping out in formal, how is that a disadvantage to ABC? (other than extra workload - the point being the PNMs see one chapter working harder than another)
Personally, I'm biased against formal, but that's because it has never worked on my campus, but I do realize it is a necessity on many other campuses.
So i guess i'm not much help