I'd love to learn reining. I'm still looking for an instructor in my area!
Posting helps you find your OWN balance while the horse moves, without depending on the saddle. Standing in a two point while the horse walks and trots is another exercise that does the same. I have issues with falling forward too during downward transitions. All you can do is work on your core muscles, and work on a lot of up and down transitions.
You can also try riding bareback (or stirrupless), that gives you nothing to depend on to stay on except your own strength and balance. A western saddle is a lot of leather between you and the horse, and it happens without you noticing it - you start depending on the saddle to stay on. I do it in an english saddle, and I notice it, because when I started riding, my first instructor (an endurance rider) had me riding bareback from the get go. My second instructor (english and western rider) doesn't have me ride bareback any where near as much, and I feel the difference in my lack of balance without stirrups to catch myself with.