I had not seen this thread before even though it was posted last year! I have watched an Athlean-X video about this exact subject and why chasing numbers is totally the wrong way to go about it because it messes with your head without even realising and ever since this my mindset is totally different to how I approach this particular workout.
Personally I have been working on 12x12x12 as that works for me. A short break in between because by the time I get to 12 on set 2 I am already at the brink of failure. I do full range of motion and the descent is always slow so each rep takes about 4-5 seconds. I also go below the bars on each descent. This offers greater advantage and gains vs just smashes out quick reps of which I can do a lot more, at least double.
I have been slacking since the last lockdown and because of my metabolism all my gains can be fully lost in just a week from previous
weeks of hard work! I have very low bodyfat percentage (5ft 8 @ 58KG) so all my gains are noticeable very quickly. At the moment I have been using RipRightHD's PRX sticks whilst sat at my desk working from home, as well as using my desk chair to do pseudo planche dips using the chair's armrests and then once a day will use parallettes to do deep push-ups as mentioned above.
Honestly doing push-ups (even pull-ups) properly with perfect form and range of motion every single rep is extremely difficult especially once you employ time under tension and something I never appreciated until more recently when actually watching, reading and trying. So when someone tells me they can do 50 pushups and they don't physically look like they're got the shoulders, triceps and back for it, I'm always a bit dubious
This is me 3 weeks in, obligatory duckface:
Once I can easily do 12x12x12 without any sign of impending failure I'll move onto one-armed variation and then focus on abs (dragon flag) but one focus point at a time as that's what seems to work for me!
Edit* typos/words...