Try BTN presses like Bazza said... on the basis he's actually pretty strong... if they don't cause pain. Otherwise I would make your main shoulder movement military presses, concentrate on getting strong on these, with some accessory work.
Also, looks like you have a bit too much volume for your strength level there...
At the moment I do:
Military press x 3 sets, 5 reps of 60kg
Side lateral raise: 3 sets of 6 reps at 12.5kg (dumbells, strict form) (btw progress on this exercise I think for most people is really slow)
Band pull aparts: 3 working sets.
I might add a set or two or take away one from the above...
A while ago I was doing 3 sets of 40kg on press, 2 sets of 5kg dumbell laterals, 2.5kg (yes, 2.5kg was my starting weight) reverse dumbell flyes. So that worked for me. I do these on "chest/shoulder day" which means they come after bench press sets.
I just made this workout up and haven't changed it cause it's worked... I would also welcome any criticism/suggestions, not that it still isn't working.... When I find something that works I go by the advice I read once which goes something like 'stop reading, would you rather be smarter or stronger - keep doing what you're doing if it works'.