If you're still okay running without much of any cushion, try Lems. They go down to size 37, and I know of people who run in them.
That's a good idea. I've been meaning to try them!
What size do you wear in them? I fear ordering a 38 since they call that a 6.5 and it's rare that a 6.5 fits me (mostly for width), but I fear that a 39 will be too big for running.