Thankyou so much for the detailed response. My physio recommended the very same back exercises, as well as bringing my shoulder blades together as you described for ten reps every hour or so.
One thing I may not have mentioned in the initial post, is that I only get this pain when I do the movement very slowly. When I raise my arms, thumb pointed up. When I move more fluently, like normal arm 'windmills' if you like, I don't notice/feel anything.
Given all of this, should I take time off bench pressing until the slight 'catch' and momentary instance of pain is gone? Or is this unecessary? I have not been doing much military press since it happened, though I did do 4x10 reps earlier last week. I do a strength routine in the gym - bench press, deadlift, squat, power cleans, bent over rows, and usually military press too.