Here are some neat independence ideas from Libor Hadrava of Axiom Music School.

1. Table of Time: Changing subdivisions with the hands over a 3/16 pattern with the feet.
2. Table of Time – Paradiddles: Same as above but overlaying the paradiddle pattern with the hands
3. Independence Plus Counting: Feet play RLRR LRLL, hands play RRR LLL, count aloud a third grouping!