|Hard on purpose.|
You could play the original materials in Dahlgren & Fine with the illusion that you're going to learn something the authors call “complete independence.” Whatever those words mean to you, it doesn't really work that way. The only thing we're really accomplishing is to learn to play the cymbals with both hands, along with the bass drum— a standard, core drumming orchestration— and learning to get to the drums and back to the cymbals at inconvenient times. And we're developing some facility with the left foot, in coordination with the bass drum.
Mainly we're creating opportunities for unexpected things to happen. If the premise of the Syncopation-based method is to do things in the easiest, most natural way, the premise here is to do things in ways that make no sense. Most of the stickings do not make the easiest way to execute the notes of the exercise. We're practicing inconvenient ways of playing things, systematically.
So, it's hard on purpose, and you can't do it all at once. You really have to be oriented around finding a reasonable workout for today. There is no finishing it— there's nothing to finish— and no particular way of doing it that is going to make you great, while another that will screw you up. I don't see a particular need to develop a lot of speed, or to work on the harder exercises much more than the easy ones. As long as practicing the method is a moderate pain in the neck, that should mean there is improvement happening.
Terms in the following notes: the system is a combination of exercises and stickings. The exercises are sets of notes played on the drums and cymbals; the stickings are which limbs you use to play them— specifically, which hands; the parts for the feet are preset by the exercise.
People seem to like the idea of “setting and forgetting” an ostinato, and then playing other things “over” it. For this system, I think it's better to pay attention and account for every single note— learn the exact sequence of combined limbs, and hit them accurately. This can mean sometimes working through things only a few notes at a time.
All exercises, one sticking
Play through the entire page of exercises using one sticking. To get your initial basic familiarity with the system, do that with the first set of stickings.
One exercise, all stickings
Run all the stickings with one exercise. This may be necessary as you get into the more complex exercises— one at a time, learning all the stickings for it. Again, early on, you could learn the first two exercises this way, using all of the stickings.
Make obvious edits and additions
To keep the introduction to the system a manageable length, I did not include every sticking combination forwards and backwards. Sometimes it will make sense to reverse the sticking with a particular exercise. There will also be duplicate stickings with some exercises, which you can skip.
A lot of people like to start complex exercises beginning with an ostinato— by playing the easiest part, and adding other things. I'm not convinced it's the most productive way of practicing this system. I think you should work on starting the exercises complete, with all the parts at the same time.
Another small thing that can nevertheless cause you a lot of grief. Try to go from one exercise or sticking to the next without stopping.
If you play the hihat with your hands, any BD/cym note immediately before a SD/foot hihat note will naturally create an open sound. It's a common drumming effect, and you could spend some time focusing on it. You may have to adjust the timing of your left foot motion to get a good open sound.
Moving around the drums/cymbals
Moving the drum notes between the snare and toms in a systematic way would be adding another level of complexity— and length, and unfinishability— to this system. I just improvise moves, or work on them occasionally with a few exercises, moving to a different drum on every note, according to the stock moves listed in the link above.