Just as an update on Gizmo's biting: I tried the suggestion that a couple of you gave me about giving him a bigger stuffed toy. He loved the large stuffed cat that I had, but only as long as I was holding/shaking it, which resulted in a few misses of the toy and contact with my hands. Today I went hunting and found a plush stuffed cat toy, basically just a rectangle with a fuzzy tail hanging off the back, and he LOVED it
Mind you, he was less thrilled with his other present, which was his very first collar. He kept trying to bite it off, which is pretty funny to watch. I'm sure he'll get used to it pretty quick, but until then...
thanks for the advice everyone!