Steve, if your shoulder issue isn't severe or surgery related, try shrugging heavy weights, then heavy bicep curls, do these with correct form then perform one pull up to check if it hurts. These helped me with my shoulder issue which came from muscle strength recruitment.
Andy, which exercise recruits your lats to the fullest and wants more. Intensive.
I find deadlift work my lats differently than pull ups. It's just so hard to keep the bar touching the shins and thighs as I go up or down.
Pavel, I believe you. Same goes for my lats doing OAP.
A good pullup for me is 210 bodyweight + 80 lbs = 290 total. A good deadlift is 435. So the deadlift is 50% more total weight. This suggests prioritizing deadlifts for a general "pull." And just including a few pullups to let the lats and elbow flexors catch up.
Ab wheel rollouts seem to work my lats pretty hard.
What really help wake up my sleepy left lat was a little exercise from the physical therapist. It made my shoulder stop hurting. Stand while holding to a suspension trainer with one hand and lean directly sideways with arm straight. Then bring the elbow to the side of the ribs so the tricep and lat come together.