How to tension toilet handle nut without handle sticking?
Buy the kind that look like this:



Notice the 'ears' that wont allow it to sink into the hole and the full length square body that would make it impossible to over tighten it (at least, not enough to inhibit functionality - you'll have broken it way before then).

If I had to guess, you're still using metal ones or you're dealing with offset (angled) toilets, the handles for which are also available in plastic. 

There's lots of different kinds out there. I think you're getting the wrong replacement type for the kind of toilets you have.