DFC et al,
I'm a glider and "self launcher" (B737) pilot.
I don't agree that pushing will ever extend your glide or help clear obstacles, UNLESS you are flying into wind and the wind strenghth decreases with altitude.
Flying at best L/D will always provide the longest still air glide. Flying a speed adjusted for wind will always provide the longest glide in the prevailing conditions. "Pushing" and increasing speed will reduce the L/D and shorten the net glide.
HOWEVER, if the requirement is to clear an obstacle, and the glide distance past the obstacle is not an issue, a short duration "Pull" will temporarily reduce the sink rate and glide angle. Once stable at the lower speed the aircraft will resume a stable glide at a steeper angle.
So I think the "Push" is of no value, but the "pull" may be.