Calling all personal trainers

[Seajay]

...just regular athletic shoes (and, no, I don't get sore arches).

If you can imagine your IT band flicking back and forth over the lateral condyle of your femur....getting more irritated with EVERY pedal stoke. You can understand the problem.

Stabilizing the foot on the pedal is important.
First by getting rid of flexy (unstable while cycling) running shoes.
Second by providing support to the forefoot. Many of us have a varus forefoot which can "collapse" as we push down on the pedals. This sends the knee inward with each stroke.
It's really not supposed to do that.
However, so many cyclists do it that it is considered "correct form"....It is not.