The way my instructor has me engage my horse's behind is by "imagining" (bear with me here...) that I have two metal rods from my hip bone to my seat bone on each side, and my saddle is a huuuuuge magnet. When I want impulsion, the magnet "turns on" to pull my seat bones down, and I sit deep to push forward with my seat (does that make sense?) in rhythm with the horse's movement. Even if you're posting the trot-- on that down beat, you're sitting deep (not plopping down-- it's different) and squeezing.
Additionally, I applying rhythmic leg encouragement (for the walk I kind of push the barrel side to side between my legs, for the trot it's a squeeze, squeeze, squeeze).
All of this pushes my horse into the bridle. Assuming he is accepting the contact, pushing with your seat (and leg) in this manner will encourage them to be more forward and get that "recycling" going that you're talking about.
I hope that helps!