HERE IS THE FIX -- VERIFIED BY ME!
Thanks to Jonathon Dunford! I was able to flash my 12.2 back to 4.4.2!!! I am copy/paste/editing Jonathon's steps here, specific to SM-P900:
1. Download Samsung Kies or Smart Switch, and back up device data. Remove the microSD card from the device if you have one. Make sure device has a good charge (at least 50%).
2. Go to
Download firmware: P900XXUANI1_P900BTUANI1_BTU - SamMobile -- this build is for the UK, but the build number (P900XXUANI1) is correct. The file will be in .zip format and is 1.6GB, so be patient.
3. Once the download is complete, extract the firmware file to a place you will remember, like a folder on your desktop.
4. Download Odin from a reputable source like Softpedia or another site that tests its downloads for malware.
5. Make sure your device is off and disconnected from your computer.
6. Open Odin. Under Options, only "Auto Reboot" and "F. Reset Time" should be checked.
7. Click the "AP" (or "PDA") box and browse for the extracted firmware file (P900XXUANI1_P900BTUANI1_HOME.tar.md5).
8. Press and hold the following buttons in order: Volume Down + Home + Power. Keep holding them until you see a screen that says "Warning!!" at the top.
9. Press the Volume Up button to continue.
10. The next screen will show the Android logo and say "ODIN MODE" at the top left.
11. Now connect your phone to your computer via USB.
12. In Odin, look to the top left and wait until you see in the leftmost box "COM" followed by a colon and a number, such as "COM:4". The number doesn't matter. Once you see that, you can proceed.
13. In the Message box in Odin, you should see several lines of text.
14. Press Start in Odin.
15. Odin will begin processing, and on your screen you will see "Downloading" with a status bar underneath.
16. When Odin is successfully finished, you will see in the Message box "All threads completed".
17. Your device should begin rebooting. You can disconnect from the computer.
18. At this point, my 12.2 got stuck on the "SAMSUNG" logo page, and wouldn't boot properly. I resigned myself that I'd need to do a factory reset, but oh well, better to have a tablet with a non-functioning keyboard than a non-functioning tablet. But upon factory resetting, I found myself in 4.4.2!!!
19. Power down machine.
20. Boot to restore menu by pressing and holding the following buttons in order: Volume Up + Home + Power. Keep holding them until you see the "Android system recovery" screen.
21. Press the down volume button until "wipe data/factory reset" is selected. Then press the power button to select.
22. Press the down volume button until "Yes -- delete all user data" is selected. Then press the power button to select.
23. After the wipe is complete, "reboot system now" should be selected--simply press the power button to select.
24. Upon boot up, you will find yourself setting up the tablet as if it were brand new. Once you can get to the settings screen, you will see that you are running 4.4.2.
25. Connect your keyboard/mouse/whatever!!!!!
26. Restore your apps from Kies/Smart Switch.
NOTE: since this is a very old build, you will spend several minute downloading updates, typically pushed to your device via the Google Play store. This is a small price to pay to get your bluetooth devices back. Big price to pay for Samsung's terrible QA, but... my keyboard and mouse work!
Kudos again to Jonathan