yes… cittaja rupa are indeed responsible for movement. And kalapa don’t move. There is not time to move. I think I say in my abhidhamma book (somewhere) that just as computer monitor pixels don’t move, the same is true with the 3D pixels (kalapa) of our material world.
It is mind boggling to think in this way, but we should. When I walk and have mindfulness to do so, I contemplate myself similar to this (remote) picture (but monk and male). I’m glad I could find the picture. I’ve remembered it for years. @hannibal perhaps this can be an abhidhamma meditation contemplation for you?