One more either clue or red herring. I injured the same shoulder about 3 years ago doing lying dumbell triceps extensions (when I didn't know any better), and when I started doing dumbell presses, I had to start at 10# per arm, limited by the right arm. Now, when I do barbell presses at limit, my right arm is typically the limit on lifts (to the extent that the barbell is tilted towards the right, as that arm struggles to push the bar up).
I also have more trouble on lockout on that arm (which may be because of the injury or lack of lockout may have exacerbated it).
Also, the pain snuck up on me -- that is, no obvious trauma on one lift, more of a gradual ouch that is now a barrier to my lifting.