As much of a hassle as it might be, the best way to do it is to take the head/pipe off the puppet, measure the amount that is sticking out between the lazy susan and the neck, and slice it off at the bottom. If you do that, slide the pipe back down the barrel and reattach the PVC joint under the hoverskirt so that it's flush with the bottom of the bowl, your problem should be fixed! The joint sitting flush with the bowl will lock the head close to the lazy susan, closing the gap. It might help to put a bolt through the joint/PVC pipe just to make sure it's super tight and the control rod won't pop off. If you've already put a bolt through down there, you'll have to drill a second hole higher once you slice off a bit of the bottom.
Hope this helps! It's more work, but it'll make your Servo work like a charm!