We'll take that a couple of steps farther, using a more complicated foundation pattern, BSSB-SBBS, and learning to use that voicing while reading rhythms from Syncopation. Relax, it's doable, and I think it's worth the effort.
Here's how you would voice some basic rhythms, following that pattern:
Warm up with the above patterns along with the cymbal rhythm of your choice, then practice the system using Reed pp. 4-5, 10-11, 30-32, 34-45, revoicing the top line part from the book accordingly. If doing the complete pattern is too difficult at first, try doing just BSSB-BSSB, or SBBS-SBBS. Warm up with beats 1-2 or 3-4 in the examples above, repeating.
I started doing this as a 2/2 funk/rock system, but there are a lot of other possibilities. It would work fine as a jazz thing. The bass drum part sketches an embellished tresillo rhythm, which makes it useful for some broken New Orleans funk type rhythms, or Baiao, or especially Songo— or whatever other Cuban-type styles/settings where creative funk-like playing is appropriate. The snare drum part makes a cut time funk rhythm, but also suggests the 2 side of a clave rhythm. There is the tantalizing possibility that if you made a two measure system out of it, reversing the pattern in the second measure, SBBS-BSSB, you'd have a complete clave rhythm. BSSB-SBBS-SBBS-BSSB. Play that, check it out.
Just within a regular funk setting, some of the more fragmentary rhythms in Reed create some interesting displaced groove patterns. Many of the rhythms lack that cut time back beat on 3— those patterns are useful for working on open hihat punches with the bass drum. Practice patterns that have a note sounding on beat 3 will sound most like a funk groove.
I'll be interested to try this with the other paradiddle inversions: BSBB-SBSS, BBSB-SSBS, BSBS-SBSB. At some point I imagine we'd get diminishing returns with this kind of thing, or possibly it just gets much easier and we can choose one way or another based on what it's good for stylistically.