Yeah, find a way to balance a big push with a big pull and you're half way there.
Add a hinge or squat etc and you have the basis for a good balanced program.
It doesn't have to be an either/or arrangement when it comes to weights and bodyweight work either. You can design a program around the push/pull theory and use both modalities in successive workouts or even mix it up and use both in almost every workout.
My workouts are in a constant state of evolution and almost always include weights and bodyweight work. Sometimes I'll replace the MP with HSPU and vice versa. Sometimes I do KB swings, snatches or CSP's other times I just do squat jumps or mae geri's. I just do anything I can to make it feel like I'm not working out, I do less reps than I could but finish before mental or physical fatigue sets in.
I don't really see how Bodyweight exercises would work in there. There's many Days where you have to add incremental weight on each set. If you're really set on using calisthenics, you'd have to use purely weighted calisthenics. Weighted pull ups weighted dips, weighted squats (aka any squat with weight) and maybe swings/DL.
Don't get me wrong. I'm with Tarzan here. I love HSPUs, OAPUs, and hollow body work (ab wheel, front lever,etc) but it's rather hard to precisely change the resistance as you would in a barbell.
Also I think the program works because of neural strength. Training light benching transfers to heavy benching (" easy strength") because you practice the movement perfectly. But to regress any bodyweight exercise, you'd have to change the groove itself. Elevating your hand for OAPUs, for instance, makes it more like an "decline press", not really a "lighter bench". That's fine for TNW purposes. But it might not be for this program.
Idk just my 2 cents. It might work well all the same hehe ^_^ good luck