Further investigating using Kid3, a free MP3 editor, I noticed that the ID3 tags of the source MP3 files in question already appeared garbled. I then hit upon the thread "iTunes not importing Japanese artist/title metadata" which described a very similar problem. So I followed the proposed solution (using ID3Mod2, a shareware program), which solved my problem (Note: I tried Unicode Rewriter, too but at least without ID3Mod2's help to relatively painlessly arrive with the proper, originally used character encoding, it didn't fix my problem (in other words, it might have worked had I known the exact encoding; choosing AutoJIS in Unicode Rewriter, didn't yield the proper encoding)).
There were still a few steps involved to get this problem corrected though, as you have to manually tell ID3Mod2 which encoding was originally used to encode the garbled characters, which may or may not involve some guess work on your part. Having heard of ShiftJIS before in context of using Japanese input under Windows, I tried "ShiftJIS" which looked mostly correct (i.e., the "Title" and "Author" fields shown in ID3Mod2 now appeared in Japanese characters) except that for some songs "** CAN NOT DISPLAY **" appeared for some of the fields. Selecting "ShiftJIS_X0213_00" allowed the "** CAN NOT DISPLAY **" text to disappear for these files, too.
Scrolling through the correctly appearing list of files in ID3Mod2, I noticed that some files had an empty Title and sometimes even Album field. So as a precaution, before saving the songs with the now corrected ID3 tags, I removed those from the list of songs in ID3Mod2 (by sorting the list of files by Title and removing the block of files with an empty Title (minus a few that had an empty Title, empty Artist but a non-empty and properly appearing "Album" field (which only appeared proper when using the "ShiftJIS_X0213_ 00" encoding (that is, toggling the Encoding to MacRoman, caused this field to appear improper for these files))).
On a side note, iTunes offers a "Convert ID3 Tags" function that sounds like it should have fixed my problem, alas, blindly trying various options offered by this function didn't seem to have any effect. That said, before you try ID3Mod2, you might as well give that a shot first, perhaps it works for you.
