I agree with the Mohair girth, but do make sure it is 100% real Mohair, not a less expensive Mohair blend. It makes a difference.
Depending on the horse's conformation and the saddle, it may be helpful to change it to center fire rigging to get the girth out of the elbow area.
My thin skinned TB appreciated having the girth slightly loose, but she has big withers to keep the saddle in place, helped by a breastplate and crupper. I keep gall salve on hand, just in case, but I haven't needed it since switching to Mohair. It is a good idea have a couple girths on hand for multiday rides, especially if sandy or muddy.