I'd try to find a podiatrist who rides or even runs. The advice to stop riding is premature, I think.
I'm surprised you have ball-of-foot pain with those MKS pedals. With soft soles, I'd expect pain where the pressure is - at the ridges. I rode SR quills (see link below) for 30 years with hard, stiff soled Puma touring shoes and Nike cycling shoes, and I rarely experienced foot pain. When my last pair wore out, I tried riding in running shoes, and 20 miles was my limit - my feet hurt too much to go farther.
Based on my experience, I think stiff-soled shoes will make a world of difference for you. But ...
I went to pinned, flat pedals, though, because I couldn't get shoes that worked for me. I tried one pair each of Bontrager and Bont shoes without cleats. They worked OK in the toeclips - the problem I had was that the soles were so slippery that I had trouble staying upright when I put my feet on the ground, even after a couple of hundred miles on the shoes (that's a couple of hundred on each shoe). The touring shoes had some rubber on the soles. The Nikes didn't, but the soles very quickly got rough enough that they didn't slip.
I see your main options this way:
1) MKS pedals, stiff-soled shoes, old-style cleats, toe clips, straps -
almost guaranteed to stop the pain, if you've diagnosed the problem right. Alas, many people do not like cleats.
2) Freeriders and new pinned, flat pedals like my DMR V12s, Raceface Chester, Crank Bros Stamp, Wellgo MG1, etc. - this will probably at least reduce the pain and may prevent it altogether, but no guarantees.
Photos of SR quills:
https://www.ebay.com/itm/31361423216...rchantid=51291