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.

Singing and playing music is a big part of my meditiations. It took a long time for me to be able to even attempt silent meditation. I'd suggest looking into Tai Chi. From what little I know about the philosophy behind it, it's big on channeling and moving energy and the slow, controlled movements might help keep your brain chatter occupied.