You have a ton of options…
I'd recommend looking at somewhere like Joshua Creek (Axis/Turkey) but I'm not sure how many axis hunts they're planning on this spring due to freeze. Accommodations are phenomenal!
Some of the other bigger ranches would also be able to accommodate a big group and have nice amenities, like RecordBuck Ranch (Utopia) and of course the Ox Ranch (Bracketville/Uvalde). The JL Bar in Sonora is really nice according to one of my buddies and it's almost like a resort.
The King Ranch would certainly check your box for Nilgai and Turkey and I am sure they have nice amenities but I know nothing about them.
Quite a few other options that I am sure will be brought up by other posters.
Good luck!