First off welcome!
All that was already said (body rows with desks/towels, negatives) will help you. I'd suggest if you don't have a sturdy stool to try using a stability ball to help you up or surgical tubing/pallet bands. Otherwise use different substitutions throughout your workout when you can't continue with pull-ups i.e. body rows, slow negatives, jump-ups etc. and try to vary your grips i.e. wide/small grip palms facing in/out and one palm facing out one in. This will help strengthen other helper muscles, alleviate chances of injury and you will find that switching grips throughout D1 will make it possible to get closer to completing the 20 min as you're not constantly targeting the same muscles. Remember that it is OK to take a break during D1 to recover and then continue. Just make sure your clock keeps running. D1 breaks DO count against your time. You may want to try something like 5 rounds then a 1 min break and repeat or really whatever combination works for you. Once that gets easy increase the rounds before a break etc. etc.
Lastly this all takes time so don't get discouraged, the fact that you're doing pull-ups or chin-ups already is a great thing! The endurance and strength will come if you stick with it. NICE WORK!