A pre-rooted ROM of the new 22.214.171.124 software version for the 2nd-gen Fire TV has been released by rbox. You can find it here at the usual place. If you’re financially able, please consider donating to rbox to show him your appreciation for his continued work keeping all of us capable of updating our devices without losing root. You can install this new ROM regardles of what version is currently on your Fire TV 2. Be sure to also grab this MD5 file and include it with the ROM to ensure the ROM is not corrupted before flashing.
This pre-rooted version of 126.96.36.199 does disable FireStarter and FiredTV, just like the stock version. However, because you’re rooted, you can disable the app blacklist and re-enable either app by following this guide.
Rbox told me he had a chance to make progress on TWRP for the 1st-gen Fire TV and Fire TV Stick, as well as pre-rooted ROMs, so those are very much still in the works and should be released by early May at the latest.