Very little of that chunk in the middle sees unrestricted gun ownership as their number one issue. Once you decide to put guns over other issues, you are a locked in R voter, or D voter if you support gun control as your number one issue. Once you say, "I care more about owning this AR-15 than I do about Americans having Healthcare, humane treatment of undocumented immigrant children, or a competent pandemic plan," you were never going to vote D.
Never pander to single issue voters. Whether the single issue is a real belief or an excuse, they simply don't cross over even if you cave.
When you look at the adult population of Texas, there aren't that many CHL licensees nor are there that many hunters. Old school Texans like yourself still think of that old school Texas, but the population boom is made up largely of people that don't hunt. They may have a handgun in their home, but don't carry it around, and will still keep it no matter how they vote on gun control. But they also didn't move from Ohio to the Dallas burbs to be around minorities, and will use the little white lie to avoid saying that.