Oh wow, this actually worked 
I logged out of the forums one more time, both on my PC and my phone (so “completely” logged out everywhere), then re-logged into the forums on an “Incognito” tab… lo and behold the “New Post” button is now unlocked and I can reply to threads
So I assume it was some sort of issue with saved website settings/browser cookies, because all of a sudden the beta forums work. We’re off to the races 