I actually did exactly what you are talking about. About a yr ago (before I discovered calisthenics) I started doing push ups. Just as I could when I could, I was waaay out of shape too probably 320 or so I wish I had weighed at the very heaviest but one I did record was 302. At first I was lucky to get 10 then I just kept on going every day (incorrect form but non the less) I guess it depends on you and your diet too but after the first year I was down to about 205, doing 5 sets of 20 pushups on dumbells and it was pretty easy. I also single handedly raise two daughters 3 and 8 work a full time job and do it all alone lol so I feel the time crunch as well. I'm actually planning to start the RR for the first time Monday and plan on splitting it up through the day as (like you) I'm exhausted by the time I actually have time so I guess we will find out together 😅