Whether to do modified pull ups or keep it going is a personal decision. Since I always do pull up substitute, this is not an option for me. I usually increase the rest period between sets on D1. For example, I started with 18 rds in 20 minutes on L1D1 and eventually increased it to 20+ rds before I graduated to L2. Right now, I am doing 30 rds of L4D1.
Same idea on D3. I do 17 pushups in the first set take a 30 second break and do a 5 pushup set take a 30 second break etc. I will finish all the pushups asked for, some times taking 30 second break for two pushups
. I am taking 7 min and 36 seconds to complete L4D3. I have many more weeks to go before I can get it under 5 mins. Every week I target to increase the number of pushups in the first set or reduce the rest time between the sets. Every week I aim for about 3% improvement.