It sounds similar to a pain I get in both feet (but more on the right) after biking for extended periods. This only started happening when I started doing more things (including running) barefoot or in barefoot type shoes. My podiatrist thinks it's because my bike shoes are more structured, stiffer and with less room for toe splay when I press down on the pedals. Because it's not really a weight-bearing sport, it takes quite a while for the pain to surface. Pain is alleviated almost immediately upon removal of my shoes and walking around in sock feet allowing my toes to splay out naturally. In my case (and maybe yours), tendons are getting squished and eventually, they start to complain.

I would bet that if you went a few days without cycling, the pain would be gone for the next ride and probably won't resurface until you do another longer ride. That's how it works for me. (I also wore specialized carbon road shoes). Unfortunately, I don't really have a solution for you. My podiatrist wanted to cut my road shoes but before I got that far with him, I got injured and had surgery so it's a whole new game for me now.

I hope you figure it out soon!