Bt fixed itself?
OK. Riddle me this. I had the same issues as the OP, i.e., Bt mouse not pairing and not even clickable, as shown in his linked video. I can't tell you exactly why I did it, but I unrooted and relocked. Then I got the OTA 4.4.2. (Instead of the one I flashed.) Used everything for a few days. Mouse still refused to pair. Just now I unlocked and rooted. Guess what? Mouse paired and connected without problems. I've now got a Bt mouse, keyboard, AND headphones running just fine!
I'd like to shut it all down to see if things reconnect automatically, but I don't want to press my luck.