for what it's worth, I've been suffering from what appears to be a supraspinatus injury since December of last year (from heavy dips). Been to a couple of physios, one of whom nodded their head when I mentioned presses as a rehab tool (but still prescribed band work). The other was against presses, not because of impingement, but because apparently the press works the traps too much, and this creates imbalances (I'm not making this up, I have a vivid memory of these words). This latter physio prescribed all manner of nonsense, including lying on a swiss ball and making superman poses.
Anyway, I tried all sorts of stuff - presses seemed to help a lot, but one of the problems was that the smallest increments my gym affords me was too much at a certain point (adding 1 kg was the difference between no pain and pain).
So four weeks ago, I ordered a barbell, a pair of 10's, 5's, 2.5's and fractional weights (as light as 1/4 lb plates). Did high rep presses twice a day, in the comfort of my bedroom, with as perfect form as I could muster. As the days passed, and the weight increased I reduced the volume and frequency. Before I ordered the barbell, a single rep of 56 lb would cause pain. Today I pressed 72 lb - three sets of 7 reps. No pain. My plan is to keep at this until I'm lifting my regular sets of 5.
Remarkably, my shoulder is substantially better than it has been since the injury, and I've been able to incorporate weighted dips once a week without aggravating the injury. This stuff REALLY works. I can put on my backpack, scratch my back, dry my back with my towel without pain these days.
I was going to wait until the shoulder had fully healed and write a post, but this seems like the right place to do it. So, on a personal note, thank you Mark. You are directly responsible for this.