Nigerian Uromastyx... (humidity problem)

We recently acquired a juvenile Nigerian uromastyx which I had temporarily set up in a small Exo-Terra without any problems whatsoever other than it was a little small for him/her. He/she is in a 20L now (just a little guy, so he has plenty of room for now) and for the life of me I cannot get the humidity down. It keeps hovering around 60-70% even when its hotter than 7 hecks as its supposed to be (basking 120ish/cooler end low 90's) and not a drop of water in sight. I've put 3 different hygrometers in it and all read the same, so I am pretty sure its accurate and not just a bad hygrometer. What in the world am I doing wrong here? I've never owned a critter that needed such extremes, so I am clueless at this point. Everything else I've ever owned was tropical or moderate and never had any problems keeping an acceptable climate. I'd appreciate it if anyone can give me some ideas on how I can lower the humidity for him/her. Thanks!

What is the substrate?

Cage carpet. Tried newspaper and paper towels too, same results. I've heard good stuff about bird seed, but would that really make a difference? Wouldn't that hold in whatever moisture is in there? Sand is not an option. Been there, done that with bearded dragons and leopard geckos.

Hmm...I use sand and have never had a problem. Of course, Uromastyx aren't insectivores, so the risk of impaction isn't really an issue for them like it is for beardies and geckos.

I also live in Mobile, Al (fairly humid compared to the rest of the US).

I do know a lot of folks who used bird seed as Uro bedding, but like you, I do not know what effect it would have on humidity. Another alternative is just having slate tile/rock on the bottom.