To clarify: Clever would be to to spend several days hunting down a bug that will affect 0.0001% of your users, and has an easy, well-known workaround?
It's going to affect 100% of your users in 2038. So yeah, if you see the game as just a product with a limited lifecycle then sure you can make excuses for cutting corners. If you see the game as a piece of art then you should have some interest in it working in the future. It's not like time_t overflows are rocket science.
Although the most clever solution would be to not have any bugs in the first place ofc ;)