Guys, this weird method worked!
Before touching the live system I made a quick test on the backup hardware by replacing the config file in the /conf directory and rebooted. As expected, interface mismatch happened, but during boot I fixed that with dummy values of that different hardware to let me in.
I noticed that there were package problems, the config file brought the already broken package list from the live system. I compared the initial dummy config file with the one coming from the live system and copied the XML part referring to the packages from there. Brushed it up a little to keep packages's configs - except NTP which was completely changed during the update.
Afterwards, a new reboot, new interface mismatch - but everything else seemed to work fine.
Today I took the live system down, plugged in the newly created card with the patched config file, booted - et voila! It worked! Apart from having to click Save once in the NTP service settings page, everything worked fine! No interface mismatch or any other errors.
Now I have a fully functional, fresh and up-to-date system, and during the process I had virtually no downtime on any of the services offered by the system.