I had terrible problems with my feet, exactly as you described, progressively getting worse after my accident. I now realise it must have been from the diabetes which was undiagnosed for a long time.
I did pretty much all the same things as you have done.
Thick padded socks etc.
The biggest difference in the comfort of my feet was buying MBT shoes. They stopped a lot of the pain, particularly that feeling of walking on your bones.
They are expensive but so worth it.
I'm now in a wheelchair so have no need of shoes for walking, which is just as well as the pup has just chewed up all three pairs this month.
Now reduced to fluffy slipper boots
but they are warm and comfy.
I had two open wounds on the bottom of my feet from 1996, that wouldn't heal. I got one to heal in 2008, but the other would never heal, until this summer when I was eventually diagnosed with diabetes. I found this one healed after I had kept my sugar levels normal for a few months.
I have also found that Vitamin E with mixed tocopherols help with the burning pain.