Strategies for side sleeping with Ozlos?

I know they're just about the lowest profile ear buds money can buy, but I'm still waking up in the middle of the night with sore ears from side sleeping. I use the right size and they're in my ears correctly.

Does anybody have any tricks/hacks to take just a bit of pressure off my ear when side sleeping?

A quick Google search uncovered mostly a bunch of weird circular pillows - I like my pillow, I don't want to abandon my pillow.

In my head the solution is some sort of headband that has a small amount of padding going around the whole ear to form a bit of a cavity. But I don't think anything like that exists.