I understand, but if you reverse the channels, you can wear the headphones reversed. Depending on the physical design of the headphones, this may not may not be feasible (if each side conforms to that ear). If it is feasible and you can reverse the headphones and reverse the channels, problem solved, as long as you remember to wear them reversed.

I don't know if I've ever seen headphones that are reversible like that. Sounds very uncomfortable.

I think most earbuds are easily reversible. Over the ear ones might feel a little odd, but I suspect most that took the effort to be comfortable in a normal configuration (that is, have some flexibility) would be serviceable. In-ear headsets and earbuds that have an around the ear component probably wouldn't work at all.