I have a question for you.
How close to failure are you coming on the first set of pull-ups/push-ups/squats?
If you are coming close to failure, or worse yet having to give it everything you’ve got to finish the first 10 pull-ups, then it is going to be very difficult to get 10 pull-ups in the following sets.
I might suggest trying an EDT inspired workout. Basically, from my understanding, the idea is to do the same amount of work in the same amount of time, but in shorter less exhausting sets.
So, since your goal is to do 50 total pull-ups, push-ups and squats, then you would split those reps into smaller, less exhausting sets (perhaps 3 reps would be a good starting point). This means however that the rest time between sets must be kept to a minimum.
When you can do all of the sets/reps in the desired amount of time/or perhaps with the desired amount of rest in between, then increase the reps/decrease the sets. Eventually you should be able to work up to doing five sets of ten.
You could also try doing some maximal strength work. Yes, I know you mentioned that your goal is strength endurance, but maximal strength is a component of strength endurance.
For instance, I’ve been training with Captains of Crush grippers for a while now. When I first got the #1 I was unable to close it. But, I could close the Trainer several times. I thought that if I worked to improve the number of times that I could close the Trainer it would help me in closing the #1.
Well, I eventually worked up to being able to close the Trainer 12 times with my right hand and 11 times with my left, but I was still unable to close the #1. So, I decided to work strictly on trying to close the #1.
When I eventually achieved the ability to close the #1 I thought I’d try for a max rep set on the Trainer. Low and behold I was able to close the Trainer 25 times with either hand.
Anyways, hope that helps and good luck.