make sure you are doing 100% full rom and you can go a little closer to failure but don't go all the way.
Full rom example (nose and hips to floor on each push up)
Be sure to keep the 3 min break between rounds for full recovery.
I like the idea of doing this stuff really slow
Use more aggressive angles, weighted vest , bands, rings, single limb, whatever to up the resistance.
Example: subbing dips for push ups may be a nice option.
Day 2 is the strength day
If you can keep your reps in the 5x5 range you will see the most strength/muscle gains.
So find a adapted push, pull, squat that you will fail at 7 reps and do 5x5 with those.
(feel free to add stuff you like to this list) try to adhere to the spirit of minimal equipment)
one hand push ups
one hand pull-ups
one legged squat
I personally like to ad specific core work on this day either "evil wheel" or dragons.