I saw this, and I figured this was probably my best bet, but I was hoping to have an actual lawyer confirm. In any case, looks like I can get a lifetime hunting license from the state of Texas for about $1000 (+ whatever I have to do to actually get the license), and I'm pretty sure this solves my problem. Glad to hear someone else confirm this, at least
Not sure about Texas, but as a Canadian in California on H1b I was able to buy a gun after completing a hunter education course and getting a hunting license. A fellow Canadian on TN did the same.