I've been very interested in this discussion, it's topical and timely, even though I'm trying to play 90% fingerstyle meself, I think that good pick technique is essential for a different tone as well.
1. The Kaye method describes one essential point which I have not seen discussed here yet: The downstroke is all gravity, the effort is in the upstroke, this way you get a tension-release-tension-release thing going on. The idea that you let the pick "fall" gives your arm the release of tension, and the fact that it happens on the strong beat is great for bass technique.
2. In classical bow hold, the thumb is always straight, or bent, never curved hyper-extended-style. This is good for all picking technique too. It may take a while to master, but it will benefit you in the long run.
3. The area we play over (near the neck, near the bridge) gives different sounds, and that is something the player makes a choice about, separately from techniqe. The area near the neck will give a strong fundamental, and closer to the bridge will emphasize upper harmonics.
4. It is possible to palm-mute without resting your hand on the bridge, if you MUST have that sound. However playing all night with the palm on the bridge is gonna negate all this other technique. You are better off adjusting your amp tone if you want that sound.
I had a lot of problems when I was learning classical guitar technique. I've not had CTS, but I've had tendonittis, and gotten over it. (You need to see a specialist to know which one you have, they feel the same). It took a lotta work, but it's possible.