So I guess I'm asking, does anyone do any kind of meditation while moving or immediately afterward? What do you focus on? Suggestions for resources? Similar experiences? Any thoughts are welcome.

It's probably not all that unusual to do so with yoga, which I do. When I'm being all organized and disciplined, I do sun salutations in the morning and moon salutations at night as part of my morning and evening meditations. And even at the gym, I find the movements meditative in and of themselves, plus there's time specifically for meditation at the end, though they often spoil it by trying to do a bunch of guided stuff when I pretty much just want to peace out.