All right, I found the way to use Reed at faster jazz tempos. My “the way”, anyhow. I've mostly been winging my uptempo jazz comping until now— I never had materials I really liked for working on that.
We're doing the first practice method everyone learns— playing the book part on the snare drum, along with jazz cymbal and hihat rhythms. To make a complete snare drum/bass drum texture, and to make it easier to execute at fast tempos, we'll use the bass drum to break up any runs of more than two 8th note-rate notes.
I've written out the possible orchestrations of those multiple-8th runs, along with the first four lines of Syncopation Exercise 2. It looks like a lot of stuff, but with a little practice it's not difficult to do this on the fly.
This gives us a realistic comping texture, with a nice flow of chatter on the snare drum— much of which can be ghosted— and the bass drum is realistically sparse. Those bass drum doubles give us a nice Tony Williams-like thing. It's good to use the alternative orchestrations liberally, to vary the texture.
This will sound good at all tempos— for students good initial goals would be quarter note = 238 (“Elvin's tempo”, so-called by me because of Passion Dance and Chasin' the Trane) and quarter note = 286 / half note = 143 (“Roy Haynes's tempo”, because of Matrix, Have You Met Miss Jones, and half the stuff on Pat Metheny's Question & Answer).
Exercise 2 is by far the hardest full page exercise for this type of thing, so practice it last. The other seven usual pages are all manageably easy— e.g., Exercise 1 will have less than ten bass drum notes total.