you need to pickup your feet. we practice weapon works outdoor wearing shoes. we practice on uneven grass surface (slippery as hell in the morning dews) and on asphalt. you learn very quickly that the footwork on smooth tatami surface doesn't work well here. the trick is to soften your hips or the kua (in chinese term) along with the knees and ankles. stiffen those and you are in for a very painful practice.
if you know a taekwondo person, ask him/her to do a spin back kick, then watch their feet.
and yes, you need to understand aiki.
I think I get where you are coming from with the picking up the feet thing now. Endo-sensei talks about it when stepping, but I had never thought about it when doing a pivot (not a tenkan). I'll experiment a bit more.