I also once tried methods like all the above to strengthen my nails because I thought I'd never learn to play with picks. Finally I learned.
Of course it took me many tears. The first time you try to play with picks you think you never touched a guitar before. My own biggest problem was to get along with a thumb pick, but finally I learned.
There's the argument that you can't feel the strings with picks, but that's wrong. Maybe you can't but not because it's impossible, you just don't know how to do it. You'll have to learn feeling the strings by feeling the picks. (Aware of Big Spaw watching us: What do you think the girls prefer? Artificially hardened guys or guys that do the same by just knowing how to feel? And ladies: I'm sometimes dreaming of being touched by a girl who knows how to TOUCH.) I learned - finally.
There is also another aspect of feeling the strings: If you have to feel a string with the fleshy part of your finger before you pick it, you'll damp it. If you learn how to pick a string without having to touch it before that will result in some completely new sound you'll enjoy once you heard it. That will give you some completely new musical experience, and new experience isn't that bad, is it? I learned that, too.
My advice: Go through that temporary hell of learning to play with picks (to USE picks I mean, there are additional problems e.g. for players with small fingers etc.) rather than entering that open-end hell of always having to look after your fingernails. I'm sure it will work for anyone of you - finally, of course.