Buy a bit of really strong nylon string (shoe laces work well) , you can buy kevlar but it's a devil to cut and doesn't knot brilliantly, and tie one of your D rings to a stirrup bar and clip the jacket to a loop on the string, or to the D ring itself if it's good quality.
I've done this for years as I had 5 saddles in use, fell off a few times with no issues at all.
.