Shoes for Sled and Farmers?

Last six weeks been doing sled or farmers after every workout after weightlifting (cleans, etc.)
I’ve got this progressive pain in the balls of both feet that improves if I take a day off, and ice is helping. Looking up my symptoms (pretty sure its just metatarsalgia), I suspect the hard sole shoes I like for WL are not appropriate for lots of dragging and carries at my age.

Anyone else run into this?
Got any shoe recommendations?

I do all these carries indoors, walking in a big circle around my unfinished basement. It’s already sub-0 here.

have you tried inov-8’s ? They have styles that keep you low/flat, but the cushion and sticky soles on some of them make them really comfortable… I’d get the ones for pavement if you’re on cold concrete