Tightening up slowly is the first step in working with a girthy horse, but I think that's more effective as a preventative than working through an already established problem.
Last year I leased a horse that was mildly girthy. I was careful to always tighten slowly- start on one side, put the girth on the loosest hole, switch to the other side, put it on the loosest hole, switch sides, tighten one hole, etc, until the girth was tight enough. In addition, I started giving him a small piece of carrot every time I tightened him up a hole. Eventually, I only gave him a piece of carrot when he stood still and didn't complain. Then I started only giving the carrots intermittently (he still had to be quiet to get them) and eventually I could stop using them all together.
Now I've purchased my own horse, who is much worse. He dances all over the place, pins his ears, tries to nip (but can't because he's on cross ties), and will sometimes raise a hind leg in a threat to kick, particularly on the right side. With him, the person I bought him from would cinch him up VERY quickly and my vet also suspects he has ulcers (we haven't scoped him, but he's been put on U-Gard and aloe juice), so the problem likely won't go away until that underlying issue is solved, but it has definitely improved using the same technique I used with my last horse.