Great news!
I tried my.uniden.com today and it worked! Didn't need to do anything special on my end at all. As previously mentioned, Uniden was on the issue and has apparently resolved it - at least for me. I was able to successfully buy and get the 2 keys I wanted. Yayyyyy!
I will say, I surely believe there's got to be a better way to enter those long hex codes. Good grief that was tedious! Very 1960's-70's-esque. Not what I would expect via a high $ scanner. Maybe allow entry via Sentinel or something?
Anyhow, I'm done! Yayyyyyyyyy. If you've been having problems on the site, try again. It was working for me this morning.
Thanks everyone for the suggestions, tea & sympathy. And thanks Uniden for fixing your stuff!
--Pete