Thanks for the thorough advice and quick response everyone.
Something I forgot to mention in my first post: I haven't applied squash and stretch yet. There is going to be quite a bit in the rubber portion, giving it lots of flexing during the hop (and the obligatory slight suction).
So overall, what you three have suggested is making me re-think my model and rig. I don't have much experience with CP weighting, but I looked it up in a reference and went for it. The result is a slightly more natural bow, as Paul suggested. However, I don't think I completely understand adjusting the falloff of the bones - I think my problem may be the bones themselves. I have three bones in the handle, designated as body, neck, and head. I want the plunger to direct it's "head" towards an object later on. This way, I could communicate to the viewer what the plunger wanted to do. The result of this rig, combined with the splinage (which could also use work) results in the un-natural bends.
But I like the idea of dropping those bends and adding more of a bow, with more sharp bends on the compression after contact frame. Any suggestions on adjusting the rig would be great, I've attatched a picture of the current model with the falloff settings I recently adjusted, and the rig itself showing the falloff. With these settings, I can't move the bones much further than they are in the left image, because the handle begins to distort. The falloff for the middle neck bone is quite extreme, so I'm wondering if less bones would be a better solution. Or maybe I'm just doing it wrong. Any suggestions on how to improve this would be great. A more natural bow would be ideal, but I still would like to make the plunger appear alive.
Robcat, good advice on the animation. I don't know what I was thinking, going against the technique of the classic jump outlined in the animators survival kit. You're absolutely right. I'll adjust that after I get some of the issues with the rig worked out.