Based on info I’d seen on various web forums, I uninstalled the screen-saver hack and the jail-break hack (the latter is needed in order for the former to be installed) on my Kindle 3 before I installed the 3.1 version firmware version from Amazon. Now there is a 3.1-compatible jail-break available.
I took the plunge tonight and downloaded and installed it, which seemed to go smoothly (no error messages of any sort). I then installed the same screen-saver hack I’d had on my K3 before (version 0.18.N), and it also installed smoothly. I powered off my Kindle, and my personalized screen-savers were back just like before. (Since I had not deleted the screen-saver directory the original hacking had created, it apparently re-used them this time around.)
Now I’m a (relatively) happy camper, no longer having to see the infamous “dead authors” when I turn off my Kindle.