Never used them but have heard Kiowa Outfitters mentioned here. They're out of Raton, NM. Quick glance through their website and seems like they offer several hunt options that might fit your budget. I think Units 51 and 52 are easier draw but haven't looked at the odds in quite awhile.
Like I said, no direct experience with them, but another one to look at.
I'd up your budget to $7,500 for just the hunt. No tips, travel, meat processing in that amount.
