Most solutions seem to involve a change of footwear, as is the case with new sufferers. I'd agree with
@mangid, in that it happens because the shoes are too narrow across the forefoot, and a nerve ends up getting squeezed between the foot bones.
One thing to note is that your foot swells slightly over a long ride, so a shoe that is OK when tried on in the shop may still be too narrow after 50 miles. I once had foot pain that didn't start until 450 km into a 600 km audax, with that foot remaining sensitive for two or three years after.
I'd suggest trying one of the brands that offer shoes in a wide fitting. I don't think super-rigid is necessary, but it's usually only some models that come in a wide fitting, so there may not be the choice.