If you have a very fast drop time, your sled is too bottom-heavy. Are you able to take some weight off of the bottom? The ideal option, as Louis mentioned, would be the ability to move your gimbal. In doing so, you'd find the center of gravity of the whole rig (where the sled stays horizontal), then move a little more weight towards the bottom of the sled so it hangs vertical naturally. You would then check your drop time and adjust the gimbal position (and thus the amount of bottom-heaviness) accordingly.
Since you can't move the gimbal, you can do the same process by changing the amount of weight you have on the top and bottom of the sled; it's the same principle, though will take a bit longer than moving the gimbal position. If you can't take weight off of the bottom, try adding weight to the top, which will also change the center of gravity of the sled and thus your bottom-heaviness.
As for the sled acting like a pendulum when you stop (and likely when you start, too), you must use your fingers and thumb to prevent the pendular action of the sled. It will always be somewhat bottom-heavy by definition when the post is vertical, so your job as an operator is to learn the amount of pressure to apply when stopping and starting to keep the post vertical at all times (unless the shot calls for a tilt). Explained simply, you'll have your pinky finger on the back of the post when starting (to prevent the sled from tilting down), and your ring finger on the front of the post when stopping (to prevent the sled from tilting up). If you don't already have it, The Steadicam Operator's Handbook will explain further.
Hope that helps!