You recall the foundation groove from my basic two-handed method, with the hihat and snare played with the right hand only:
What we'll do is play that groove, and a variety of others, with a mixed sticking derived from pp. 8-9 of Syncopation by Ted Reed (Lesson 3, in the new edition)— the section with the linear quarter notes. We'll interpret those exercises as stickings: stems down = left hand, stems up = right hand. So line 6, for example:
You can get the stickings from anywhere, but what the hell, these are already in the book we're using and they're in the right rhythm and everything. So: play that sticking on the snare drum and hihat, like in that funk groove— snare drum on 3 with whichever hand it falls on in the sticking, all the other beats on the hihat:
Then play these various stickings with that voicing over the bass drum parts from my pages of cut time funk beats. As a warm up for the mixed stickings, I suggest playing whatever groove you're working on with RH only and LH hand only.
First just add the bass drum on 1:
Then use the parts from my various pages of cut time funk grooves. Here's that sticking played along with groove 6 from the two measure grooves page:
Here's the line 8 sticking with groove 9 from the page of basic cut time funk grooves:
And the line 10 sticking along with groove 13 from the two measure grooves page:
You can pick one sticking and do all the grooves with it, or pick one groove and do all of the stickings with it, continuing until you've done all of the possible combinations, or until you've had enough. I don't think it's necessary to do these exhaustively— certainly take note of any rhythm/time/coordination issues that arise in playing through this; to me those suggest something foundationally unsound, that may come out in the form of you blowing something easy sometime.
If you're a real psycho, you can make a sticking out of the 16 bar exercise on page 9, and play that with each of the funk patterns.