Larry welcome to the great state of Texas! I'm a fourth generation Texan so I'm pretty familiar with the way things work here and maybe I can help out in some small way.
We have outstanding hunting and fishing resources here in Texas, but as you know most land is private. Getting access to hunt without paying is difficult. The quality ranches here are either "trophy" (like a trophy wife) ranches owned by the very wealthy or actual agriculture enterprises.
The rich either don't need your money or want to get richer. Many of the real ranchers are what we call land rich and money poor. Their land has been passed down to them if they could pay the damned government's "death tax". They have discovered that their wildlife is a very valuable asset to sustain the ranch. This has resulted in the landowners managing their wildlife producing many more quality animals. Trophy deer now exist in many areas of the state where they wouldn't have been when I was growing up.
The next type of hunting we have I find disgusting. Land owners grow genetically engineered, protein stuffed, "trophies" and in my opinion unethical hunters pay thousands of dollars to shoot them.
So, how does a guy with limited assets get to enjoy the great hunting opportunities in Texas? Here's what worked for me and I realize that some of it won't apply to you. My 31 year career in law enforcement got me access to many ranches. Being station in small towns allowed me to develop relationships with the ranchers through social activities such as church membership. When the land owner knows you and your family access is much easier.
Get involved in as many traditional archery groups as possible. There should be a lot of opportunities for this in the Houston area. The more traditional archery friends you have, the greater the chances are that they will share the places they have developed with you.
Last, do as I've done in the past. Save your money, work extra, do without and get on a good lease. It's worth it!
By the way even though ranchers hate the hogs and we are being overrun with the damn things, they know that many people will pay to hunt them.