As you have written, a formal test/analysis will always detect that a monotonously increased tick counter will not be bound by an upper limit. And the obvious solution is that you don't rely on such a thing, but define your API such that the (preferably unsigned, but doen't matter) tick-counter will roll over in a well defined way.
If the algorithms really depend on an always monotonously increasing tick-counter (which I doubt), the solution is quite easy: After 2^30 ticks set a flag which raises the "service needed" light in the cockpit, taking the plane out of service until it's power cycled. By this you explicitly state that your device cannot be used longer than 120 days continuously.
Agree with the first paragraph, but in the second I don't see how requiring a periodic reboot is a solution. Your "service needed" light is a "Case closed, WON'T FIX" message made real.
Airplanes already have an elaborate schedule for mandatory periodic service. Pressing a "reset" button once every 30 days is pretty trivial compared to dismantling the entire engine every couple of years.
What made this bug dangerous is that nobody knew about it, that's the main problem that needs to be solved.
On the assumption that there's a complicated control algorithm which, unfortunately, does arithmetic on (now-then) tick-values everywhere... but this algorithm has been extensively validated to be correct on the non-overflowing case, and it will take a while to find out how it handles discontinuities in its time scale.
Then the simple "raise service-needed signal" would be a valid workaround and easily testable local change for the next two years until the extensively fixed-algorithm went through testing and certification.
If the algorithms really depend on an always monotonously increasing tick-counter (which I doubt), the solution is quite easy: After 2^30 ticks set a flag which raises the "service needed" light in the cockpit, taking the plane out of service until it's power cycled. By this you explicitly state that your device cannot be used longer than 120 days continuously.