One should not assume that the letters originated in Texas.
For example:
Copy Fellas. I’ll post more soon.
Mail remailed by The Texas Remail Service gets mailed and postmarked at Cedar Park, Texas, which is near Austin.
I think if a remail service was used, the FBI would have figured that out fairly quickly -- although I'm not sure exactly how. And, I would think that these days a remail service would be very aware that they might be used for some kind of terrorist mailing, so they'd be on the alert for such a thing.
I don't assume that the letters were sent by someone who lives in Amarillo, but I don't have information I can use to make good guesses. I think I read somewhere that at least one of the letters mentioned the Oklahoma City bombing. If I were to pick a different city for where the mailer lives, that would be my first guess.