Most of these systems probably don't even care about the real time... so it'd just be more effective to map them back to a different index and handle it with an offset externally.

https://en.wikipedia.org/wiki/Doomsday_rule

At a glance it looks like 1971 and 1993 might be good alternatives for 2038. The command line cal program agrees with where dates start each month for all three years.