Using the exercises in Ted Reeds Syncopation (ala page 37), these can be real brain twisters, at least for me they are...
Play paradiddles in an 8th note rate, play quarters with the hihat foot and read the pages with the bass drum. Then practice the same thing with the three remaining paradiddle inversions. Play the hands on different sound sources or both just the snare, up to you.
- Standard [RLRR LRLL]
- Inward [RLLR LRRL]
- Reverse [RRLR LLRL]
- Outward [RLRL LRLR]
Then do it all over again, but this time play the paradiddles at a 16th note rate while reading the 8th note exercises. Then do it all over with the right foot playing quarters and the left foot reading.
Then play the paradiddles with your feet at an 8th note rate, play quarters with the left hand and read the exercises with the right hand. Then switch the hands so the right plays quarters and the left reads the lines.
The thing to get from this, in my opinion, is...the Syncopation book is like a 10 dollar book, but with a bit of imagination the possibilities are most likely endless for you to come up with different ways to challenge your independence. And what's even better...you do not need to sit at your drums to practice this stuff, you can do it anytime, anywhere, just tapping your feet and slapping your knees...all that for 10 bucks.
I wouldn't exactly recommend this if you're focusing on a particular style, not all of it is "musically" useful, but it'll certainly help your independence and if you've got the time, why not...