I’ve had two flare ups of Morton’s neuroma within the past two years. Your case is obviously much more persistent and serious than mine was, but here’s a suggestion.
I tried pretty much everything you did: wider shoes, rest, ice, NSAIDs, metatarsal pad, an athletic therapy app’t and minimizing barefoot walking. One thing that you didn’t mention that I found more effective than everything else was a tapping/padding technique. It took some experimentation to get things right. This is the procedure I used:
Using athletic tape, tightly secure the 3rd toe to the 2nd toe and the 4th toe to the 5th toe. This should create a v-shaped gap between the 3rd and 4th toes (I assume that this is the location of your neuroma.). Cram a lot of soft padding in this gap and lightly hold it in place with more tape. The tape shouldn’t compress the toes together at all. For padding, I used women’s makeup remover pads which were conveniently wedge shaped and very soft. Keep this on 24/7 (even at night) and change it when the padding gets squashed or the tape starts to give. This virtually eliminated the sharp shooting pain I felt when toeing off. Good luck!