We've been practising the first six or seven partner practices with bokken from Saito sensei, and so far, beginners are struggling to match each other and being late, but with some of the more experienced people I've had the experience of moving completely together, as if their sword draws mine up or vice versa. I've been thinking that it feels better, but it feels like there should be a step further in the interaction where I can somehow take the initiative more. Not there yet obviously but this discussion seems to confirm that suspicion.
The kumitachi deals with taking/changing initiative. If I were in the region I would seek out Lewis de Quiros for info on them.