I use modifications now all the time and see nice results. Especially with pull-ups, doing anything any way is better then stopping. Day 1 is for endurance training, so you want to feel some fatigue and have your heart racing. Even just doing modified pull-ups (or how I do it, switching to modified pull-ups when my form becomes crap) will get your muscles working. Do as much as you can for those 20 minutes, but definitely try to do 20 minutes. Take little breaks, get into a rhythm, but just keep with it. Day 1 is for me the hardest, but most rewarding.
For day 3, it's all about personal time, so just keep doing pull-ups until you complete the goal number, then move onto the pushups, then when complete, move onto squats. You don't stop, but you can definitely take breaks. However you count your breaks. When you can do all of the exercises in order in under 5 minutes, you know you're ready to move onto the next level.