So the only way I know to verify firmware version is the Device info screen which shows 12.2.2. I see the later versions in the jailbreak thread as you indicated. For what it's worth, the
Kindle E-Reader Software Update page shows 12.2.2 as latest for 6th Generation.
Unfortunately I don't have the skill or dexterity to manually intervene on the kindle.
I tried several PW2 upgrade/downgrade firmware versions. Either no response or in one instance received a message that the downgrade version was not valid for installation. Perhaps some different version for manual firmware update might work?