I also have thick, inflexible nails, but I love them!
Currently, I like my own tone the best when the nails are short. I shape with a glass file, then smooth and polish to a high gloss on the edges with micro mesh cloths.
In my admittedly very limited experience, the most important part of my nail shaping routine is a subtle ramp that leads the string off of flesh and onto nail. If I screw that up, I get to where the nail more likely hooks the string, delays the note, and gives me a degree of unwanted attack that I have difficulty eliminating. When I don't screw up, I get a smoother stroke, a mellow tone and some options for different tone based on how I address the string. For me, it's all about shape and not length. My nail plates don't flex much that I can detect. However, the nail bed does! The nail bed is anchored to the underlying bone with some ligamentous filaments that allow for some movement of the plate relative to the bone.
I don't think it's reasonable to expect to alter the material properties of nail plates in any meaningful positive way. I wouldn't recommend "thinning" because the nail plate material isn't uniform. It's a sandwich with harder material on top and bottom, and softer in the center. If you actually thin it by polishing it down on the surface, you could easily get through the dorsal stratum and encourage flaking. If that happens, it could take a long time to grow out enough nail to reverse the effect.
"If I have seen further it is by standing on the shoulders of giants." -Sir Isaac Newton
Armin Hanika 56PF