I shopped and shopped, studied the internet and had my feet/gait/shoes diagnosed by a podiatheologist, or whatever they're called at a fine shoe store. I finally bought a pair of New Balance 877s and they fit like a glove, good support, good cushion. I went jogging in them today and iced afterwards - no pain and happy feet!
There are New Balance tennis shoes to fit any condition, but a wrong diagnosis could do damage. I guess I got lucky, and I thank my lucky stars. Feel better soon!