"Kaiten-ashi" in my understanding is really a combination of two ashi-sabaki moves. First, step forward in a tsugi-ashi, then perform a tenkan.
The ashi-sabaki we teach in our school are:
1) Tsugi-ashi (which sounds like your okuriashi)
2) Ayumi-ashi (natural walk)
3) Tenkai-ashi (pivoting in place and re-distributing weight)
4) Tenkan-ashi (common accepted way_
5) Kaiten-ashi as described above.
Good luck on the rest!