I do understand what you're saying. If I were in the OP's position, I would go with a very light set of relatively stiff hex-core strings so they're easier on the neck with less tension (as in pulling weight) but still firm enough not to feel floppy.
Let's wait and see how the OP does with the La Bella Black Nylons, which are "low tension", "flexible" and "smooth".
The hex cores would be a good starting point.
At least with the nylon tapes any fret rattle should be less audible.
