I'm 5'10 with the reach of somebody 6'2. I was letting my elbows flare out to the side which made pressing quite difficult. Turns out my grip was way to wide. I've narrowed the grip and accepted the fact that the bar won't rest on my delts (which is completely acceptable) and I've been able to increase the weight ever since. The narrower grip has allowed me to setup properly and it's much easier to keep the elbows in.
Perhaps you could take a video for a form check?