I do sarvangasana (shoulderstand) everyday, so I don't have that issue. I guess if your working your upper body a lot, you could get too tight. Here's what I would do:

do more shoulder stretches before sarvangasana, like the following: gomukhasana arms (cow faced pose, arms), ustrasana (camel), and setu bandha (bridge pose), either with or without support.
You could use more height under your shoulders. Also, go up using a wall or a chair, so you can spend some time getting your shoulders rolled under.

I hope that make sense to you.

I find the same thing, if I run or bike too much without much stretching afterwards, I get very stiff. I have incorporated a few quick sun salutations after each cardio session, and I find that those loosen me up very nicely.