You may already be doing this, but when tightening the cinch do it gradually. I put the saddle on first, tighten just enough to hold the saddle on. Then go do something else, tighten the cinch again, go do something else again
Then right before I get on I tighten one last time. My western saddle is like an english with a buckle system on both sides. I make sure I'm on the same holes on both sides. So I'm tightening one side then the other. I also lift her front legs to make sure she doesnt have any pinched skin before I mount up. Yes, She is spoiled :wink
Vida used to be really cinchy, pinning her hears and making faces when being tacked up, until I started doing it this way. She still will if she is in season but its minimal and she is just being mareish.