When I started Easy Muscle Schedule C, I faced a similar dilemma. I chose C in the first place because reaching overhead without pain was a problem for me.
The exercise selection for the push-pull days was chinups and dips. Chinup from full dead hang was out of the question for me. I solved the problem by setting rings low enough so my starting position was the start position of a row, with my arms as high as I could get them. Letting the scapula rise was also out of the question. I kept them depressed but not retracted. So from this row position, I'd pull myself up into the chinup, engaging the back and pulling the elbows as if I want to hit something behind me, and allowing the hands to naturally rotate to face my chest.
I also set the rings at about shoulder width or a little narrower than that, because it's more comfortable than a wider width.
You could also try Reverse Row Sit Back, which takes the biceps through greater ROM than rows. As with regular row, you can increase difficulty by elevating the feet:
To make dips on rings/suspension trainer friendlier for my shoulders, I keep my thumbs turned out. This seems to engage the shoulder external rotators more. It will be interesting to see how this carries over to overhead pressing.
Due to the nature of my injury, while dynamic pressing overhead has not been doable for me for quite a while, isometric pressing overhead has been fine and might even provide some pain relief. I've been using an Isochain for this but I'm sure a cheaper alternative like the Worldfit Iso Trainer could work too. 6 reps of 6-sec. holds at highest possible effort works well for me. I wouldn't advise copying the form demonstrated on the Amazon product page though, as the guy doing the press has his elbows flared out to the side.
