So, I've been trying to nail these for months. Months and months. Started on a bar, with a neutral grip and a thin low-resistance band looped over the bar and under my knee. Progressed from being able to do 0 without my PT lifting me to maybe 6 on the first set, decreasing as I got more tired.
I have since switched to rings. This works far better for a dodgy shoulder as my hands and arms can rotate through the movement. But no resistance band now as there's nothing to attach it to.
I can't do a single pull up unassisted. The rings are high (I have to jump up to grip) so I'm starting from a very extended position, although I try to keep my shoulders engaged at the bottom. We do slow negatives with legs raised, and I feel strong and controlled as I move down (although we only do sets of 5, or even 4). I don't know why I can't get up 
Other lifts I do that might feed into pull ups are push presses and inverted rows. I don't do any isolated arm work. I am struggling at the traditional sticking point - I can get up a few inches, then need a boost over sticking point, then can finish them OK.
What do I need to do to improve the middle of my movement? Thanks!