I dont think you are being realistic at all.

>Students who are at a level where they'd be learning to do the computations a calculator does, shouldn't have graded homework. And even at that level, real mathematics is more than just computation.

So, a math level less than Real analysis shouldn't have graded homework?

>Decades ago, my teachers and professors knew advanced tricks for this, like "not just reusing the test questions from last year".

Math is not the only subject. For an English class, what constant would you change so that students get a comparable exam (especially if you are going to do this between sections in the same corhort)?

>resubmitting assignments

Students are not stupid, and obviously would not resubmit an assignment for the same teacher. However, there is a significant overlap between classes, so certain assignments should be retooled for other assignments.