Everyone has problems with the military press. It's the first thing to stall on Rippetoes, it's least used with EDT... I think it's just something about the lift.
I've got a theory that, since the military press is never the PRIME lift someone wants to excel at, it's always trained at a sub-optimal time. No one starts with MP's. You start with Bench Presses. So by the time you get to MP's, your shoulders are already tired, and your focus is off. Which means two things:
One, the bar speed isn't really that fast.
Two, people cheat to get past their sticking point to get their triceps (which are super-strong) to do the heavy lifting (or lowering, as the case may be).
The fix? Isometrics. Or DE-ing the MP, but I think that's kind of a waste of effort.
Hold the bar with some weight on it at your sticking point for sets of 5-10 sec isometrics. Two or three sets should be enough. Or you could just read Dan John's article on Functional Isometrics. It's good stuff.
It may be more than you need, but when my MP was stalled, that's what I used to get it moving again, back when I was O-lifting. That and lockouts. But the lockouts weren't for my MP. That was just to mark the squat rack as my territory- would YOU approach a dude holding 315 unshakily overhead? Exactly.
Putting incline presses back in might work too. I doubt you'll see anything from rear-delt work. They're not really stressed all that much in the MP.