This looks great!
There is no “the” crosspicking movement. Are you doing “a” crosspicking movement? Yes, definitely!
I think you can see in the slow motion clip that you’re using a combination of arm, wrist, and fingers to make this happen. The reason you’re using this blend of movements is because you are trying to move the pick along a path that is more or less parallel to the pickups. The wrist doesn’t move that way on its own, and neither does the forearm, or elbow, etc. So you are naturally involving multiple joints to do it. That’s one way to look at it, anyway, i.e. by looking at the pick’s motion first, and realizing that only certain joints can produce that motion. I think that this can be helpful in understanding why particular players appear to choose one specific combination of movements when clearly other methods also work really well for this.
Anyway, nothing wrong with with you’re doing here, it looks great. From the looks of this I would say you are at the stage of not worrying too much about the movement any more and simply thinking about the end results: smoothness, accuracy, speed, musicality, and so on. Just try and feed your technique with as wide a variety of musical material as possible. If you hammer away at the same picking patterns all the time, you’re not giving the motor system much of an opportunity to iron out all the kinks. If your goal is to do improvisational playing, I would focus simply on building the vocabulary you want. That’s a job that never really ends, and will provide plenty of mechanical variation for your motor system to latch on to.
Great work!