There is no shame in tightening the girth s-l-o-w-l-y! I don't have the girth tight until we are out of the cross-ties and have walked the arena once, maybe even twice, stopping 4 to 5 times to tighten. Maybe you're moving too fast. It's FAIR to the horse to give him time to adjust to the girth, and it also helps in a horse that tends to bloat when girthing.
Instead of thinking of your goal here as being "Tighten the girth quickly without the horse getting fidgety," think instead of your goal as being "Be fair and give my horse a few minutes to have his girth tightened ONE hole at a time."
THEN, your next goal is to have him be quiet during each one-hole tightening. If he's quiet with just one hole, PRAISE LIKE CRAZY, and walk one for awhile before you try the next hole. If he jigs around, break it down into even smaller steps. Apply a little pressure on the billet straps, don't even buckle it -- no jigging? PRAISE LIKE CRAZY, and walk on for another 20 seconds or so.
Repeat ad nauseum!
Sometimes our "riding time" doesn't turn out as we had planned -- sometimes we have to instead work on a problem you're having right now. When I first started half-leasing my horse, he wouldn't stand while mounted. I often spent 15 - 20 minutes out of every hour of riding time working on this problem. He now will stand beautifully for mounting about 90% of the time, and if I was his only rider, I'm sure he'd be better, because I don't let him get away with it, but I watch as others do -- make me crazy! But anyway, I digress...... But yes, I lost out on riding time working on this problem.
Ground manners are of the utmost importance. Be FAIR to the horse, but demand good ground manners.
Hope this helps!