create a interruption-proof power
There are many different ways to make an AC UPS/battery-backup.  One of them is to always use the battery/inverter to power the load, regardless of the input power, and make the charging circuit capable of charging the battery faster than the UPS's rated load.  This eliminates most concerns about switchover behavior, at the expense of some efficiency.  You might do something similar with your solar rig.

Surely there's a 12V fast charger that can run from a solar panel...