Rick, Thanks for the tips on stretching, etc. FWIW, Segovia started playing [full-sized?] guitar at about the age of 3. I'm sure that stretching and joint bending exercises are especially effective if you start them at a vey young age. Better late than never, though--right?
As for hitting the strings vertically, that's about the only way I usually can hit them, since I have no backward bend in the first or second joint of any of my fingers [except a smidgin' on the pinky]. [That's why I have to cut my left hand fingernails off practically to the quick, to keep them from getting in the way.]
The wrap-around thumb used to work for me on some chords, until I developed arthritis in the first joint on that thumb and can't do it any more.
I have an old Martin 00018, which has a very small neck, and I use extra light strings. Both these things help. Do you know of any good guitars with thinner necks?
Also, are there some open tunings that are especially advantageous to folks with small hands?
As the arthritis in my left hand increases, I think more and more about swithching to dobro-style playing, with the guitar face up, so I can chord overhand. Seems like this might make some stretches easier. But it means re-learning all the muscle memory that I've been storing up over the last 40 years.
Necessity, of course, is a real mother. I didn't start to get comfortable with barre chords until I accidentally sliced the end of my left index finger off a few years ago and could not play "C" any other way for a while. Now I slide the basic F [barre] up and down the neck with ease. Similarly, since I often find some full chords hard to to, I've taken to substituting melody runs in those situations. Thus, chording problems have facilitated my progress in playing instrumental melody riffs.