Thanks for the tips. I'll give monkey shrugs and rollouts a go.
Down and back is limiting me because the lats overpower the traps. A program with a heavy dose of "down and back" makes the lats overactive. In order to get overhead you need strong upward rotators, which are antagonists to the lats. The lats are responsible for extension and adduction whereas the upward rotators abduct and flex.
Most PTs will say that you shouldn't even train overhead unless you can pass the true shoulder flexion test (which I can't). Otherwise you're just damaging your shoulder and spine simultaneously. I think they say only 1 in 20 can do this properly.
https://ericcressey.com/strength-training-programs-pull-ups-essential
Notice how he says for people that are downwardly rotated and can't reach the wall to actually shrug up to help facilitate more upward rotation. Most folks think their upper traps are taut and overactive, when it reality most people have overly lengthened upper traps and they only feel tight because they are on constant stretch. Usually it's the levator scapulae that's tight which is a downward rotator and gets mixed up with the upper trap.