Ouch... (I live in fear of this with all the 'wall warts' I have around... even though I try to label them)
as you say if it run patches, with power but just not USB comms still useable... still great for an FX board, or midi utility.
build a couple of hardware buttons to switch patches, and perfect to leave in the studio as a utility - just prepare the SD card on another axoloti. (as Ive got a few axo boards, I do tend to leave a couple of them for 'fixed' use anyway )
one thing to consider.. before you upgrade next time, you will only be able to run patches off the SD card that are built using the same firmware version.
(so keep a backup of the '1.0.12' axo, it'll be no hassle switching your 'building board' between 1.0.12 and the newer version regularly, I do this all the time)
this leads to two questions for @johannes, about upgrading firmware without the patcher/usb
(which might give you a way to upgrade it later)
a) the 'user firmware' upgrade procedure, basically puts a patch on the board, which then makes it load a new firmware... (a bootstrap process) - I wonder if it would be possible to adapt this, such that this bootstrap loader could be put on an sdcard, and then moved that card to the 'sick' axo, such that it can upgrade from the card.
b) is it possible to upgrade the firmware via the SWD port?
jaffa you'd need an extra dongle, so it may not be worth it, and its going to be a pain/possibly complex
(obviously, not much point in spending huge amounts of time on this, for one board - but I think its interesting hypothetically)