If you want to slowly divest yourself of your collection I'd start renting tables at gun shows which are a great place to buy and sell militaria. In Houston you've got one next weekend and one in Pasadena in September.
https://gunshowtrader.com/gunshows/texas-gun-shows/
Probably the best venue is to set up a booth at the next Museum of the American G.I. annual military show at College Station.
Living History Weekend - Museum of The American G.I.
The next biggest event is the Camp Mabry Living History Weekend in Austin. They used to allow vendors, but I haven't been there for a spell so check first.
Camp Mabry Living History Weekend The Texas Military Forces Museum
Lastly, try some of the auction houses in your area which can be found on Texas HiBid:
Live Online Auctions in Texas | Hibid Texas