You MIGHT find something in the "Misc Woodwind Ensemble" category to fit. I doubt it, that's a really odd group you have there.
Your saxes could maybe find a sax trio, especially if one of the tenors is willing/able to switch to alto or bari.
Your clarinets could find a trio, if they can recruit one more friend.
If that doesn't work out, there are other competitions that are less strict about instrumentation and will let you sub in as needed.
I've been in your situation, and I feel for you, but UIL is very inflexible about this rule.