How about multiplying switch limits, calculated by the amount one switches sides per a tour?
For instance, first limit is only two hours.
But second time you try to change, it becomes four.
Third time 8, fourth time 16 hours, fifth time 32 hours, sixth time 64 hours.
I doubt anyone besides the "gypsies" would ever need more than two~three changes per a tour. If someone wants to just try each countries out, the maximum limit they'd face is actually less than current 12 hours. But a frequent side jumper with dweebey intent - more than three, four jumps and it's going to be a helluva lot of time for him to wait.