Upon further brooding, I noticed a certain bounce to my screen as well. I don't believe it was as pronounced as others', but it was there and, anecdotally, it seemed to worsen the longer the machine was open (perhaps the hinge continues to stress when fully extended).
I took a piece of 16-gauge insulated wire, cut it to the length of the Gemini hinge and laid it in the groove of the hinge on the machine's bottom. I took an equal length of electrical tape and secured the wire in place.
The effect is to distribute the weight of the screen between the taped wire and the hinge (rather than the hinge bearing all the weight itself) when the device is resting on a surface.
I've only done this a couple of minutes ago, but so far, I have no more screen bounce, no matter how fast I type and no matter which keys I use (I generated more screen bounce using the keys closest to the screen).
It looks pretty ratchet, but my real concern is: will this workaround persevere after taking it in out of my front pocket 20 times a day?
Jake
EDIT (Sept 3): my initial use of 16-guage wire and electrical tape could not withstand the travels in a front pants pocket. I'm now using a length of wire clipped from a coat hanger to rest in the hinge's groove, secured by black duct tape. So far, it bears up very well and provides remarkable stability, no screen bounce at all.