Are you allowed to say what software it is?

There were old tools like NAG-BUSTER by Erik Famm which would disable those kinds of checks.

Nag Buster is only programmed for application-specific fixes. I'm using Book Librarian by TurboSystemsCo. I wish I could just track down the original programmer but his twitter hasn't been updated in years

Had a quick look at it (Book Librarian Plus(?) v5.57.00, found on archive.org) just now. The expiration date check seems bugged. It says it will expire immediately if you turn back the clock, and the very next time I ran the program it did, in fact, behave like that (disabled menus) - but after that it would work just fine, everything enabled and showing a full year of eval time left (can go further back, seems to be unlimited but shows '###' with days > 999). So the way you'd do this is, set your clock to some years in the future, install the program, run it once to start the eval period, turn back the clock, run it again and have it complain once, quit, then run it again.

Nice work elszgensa! That's very persistent of you, I would have given up after it disabled menus the first time 😁 Did you try again due to some previous experience with other software that behaves that way?

I spent a little time checking if other cracking software I was aware of supported this tool but didn't find anything.

Nah, hadn't seen this particular failure mode before, just lucked out. But developing and testing software for a couple years teaches you a few things, amongst those that stuff that should be deterministic... sometimes isn't. Never work with assumptions, always verify, repeatedly if there's time.