Proper technique problem w/ left hand

It sounds like you need to raise the headstock - if I get what you're describing, your first index knuckle is probably over the third or fourth string - you want it over the second. Dropping the wrist wil also fix it, but that leads to the unnatural motion you've already found.

Ah, so there's no real good way to play with good technique and have it on your right leg like a regular acoustic or electric guitar? I guess I should have mentioned that, I haven't been putting it on my raised left leg.

The position for classical is very different from acoustic or electric - you have to hold it differently to get the reach you need, and to handle barres (since the fretboard is dead flat)

I've seen some classical guitarists put the guitar over the right leg, but with the foot raised on a stool. That always seemed awkward to me... I use the 'traditional' position, with my left leg crossed over the right, and the guitar's waist on my left leg.

Actually I don't think I'm talking about the same first knuckle as you. What I mean is that instead of my fingers curving the way that would make a fist, they end up more going the opposite way (like uncurling the fingers from a fist far enough that the joint connecting the base of the finger to the hand is going the other way). And the pad of my hand right below where the fingers join gets too close to the neck and touches it sometimes. It's like this when my wrist is straight and the hand assumes a more naturally curved position when I bend the wrist in towards the underside of the arm, but then my wrist is bent which is bad too. I tried putting the guitar in the correct classical position but it didn't help much.

Sorry if this is confusing, I don't seem to be able to explain this as well as I'd like.

Use a strap while you are sitting and make sure its tight enough to do some work with yor knees up. You don't need to have any certain positionwhile you are playing.

Hold the guitar while you are siitting and move your knees up and down while you experiment with leaning back and forth. Once you find you own optimal position, improvise with things around you house to replicate the position you are most comfortable with.

Remember, though to get better, being able to play in any position will improve your skill dramatically. Once you can play with your wrist and fingers in any sort of position, you will be able to master the fingerboard with your eyes closed.

A strap isn't the answer - classical guitars aren't fitted for them (and don't have the same support as a steel string, so don't put an end pin in one)

It sounds like you need to play around with the combination of thumb position and neck angle - lowering the thumb position (towards the floor) will put more arch in your fingers, and raising the headstock will compensate for the wrist movement that lowering the thumb will create.