In response to my whinings about Moodle, I got some help. One Moodle vet who offered help asked me to invite him as co-administrator of my site so he could see for himself what was going on. He even went to the trouble of installing Moodle using Fantastico, as I had, so he could see how Fantastico distributed the various Moodle files, especially the language files. He discovered that the new Moodle upgrade, which creates a separate language folder in a folder called "moodledata", under Fantastico this folder is called "uploaddata", and (in my case at least) was still inside the "public_html" folder, together with all the other language files created under the previous (1.5) version of Moodle. He hypothesized that one or more of these language files was/were interfering with the charset selection, and so he suggested trashing the old language files except "en" and "en_utf8".
This solved one problem: the encoding of the pages in Japanese EUC, instead of utf8. However, it failed to allow users to be able to save and recall pages written in Japanese utf8: the text always appeared as ?????
A few days later, a collleague who is also using Moodle showed me how his is set up, and I was able to re-organize how my front page looks. We also suspected that our php and MySQL versions were not up to the required versions, and that might be the problem. However, my server (at least) IS up to the required version, so that is not the answer.
I think I will put this on the back burner for a bit, and simply tell my students they can only post in English for the time being.