I implemented this idea, but ran into management issues with the lock file. (The lock file was not deleted properly, it was overwritten, etc.)

Neither of these situations is a problem. The lockfile is only there to be locked. If it is absent, then there is no lock. If it is present a lock should be attempted. The contents of the file (if any) are irrelevant.

You have presented an alternative which is, by comparison, brittle. It relies on shelling out a lot and we know from experience that this can lead to problems.

If managing your own lockfiles with flock is too tricky then why not simply use Script::Singleton as stevieb suggested here? That's a simple, reliable solution.