Another minor tweak on a normal Reed method, in a jazz feel. It's good to have some easy options to relieve the tedium, and to bring more of the texture of real playing into it.
Do this with the ordinary Reed snare drum comping method— jazz rhythm on the cymbal, melody rhythm on snare, 2 and 4 on the hihat. But now let's hit the last note of the melody as an accent on the cymbal and bass drum— usually on 4, the & of 4, or the & of 3.
Here are a couple of lines of Reed played this way:
Catch the accent with the shoulder of the stick in the riding area— that's a technique you never hear discussed, that I do all the time. It's a normal part of playing the ride cymbal.
While practicing you can hit that accent every measure, or every two measures. In real life you'll do it more sparsely of course.
Making that accent disrupts the cymbal rhythm, so come back in with it on beat 1 of the next measure, except with an accent on the &of 4; then play the cymbal accent as a tied note, and come in on 2. But play the complete melody rhythm on the snare drum regardless. You might not ordinarily do that in real playing, but doing it in the practice room it will help you perfect the timing— it's easy to rush from the & of 4 to the 2.
I didn't include a hihat part in the examples. You could keep it going on beats 2 and 4 throughout this, except maybe when the accent is on the & of 3, you could drop it out on the 4. Do what you want.