OK. As per the advise I received here I've tried the same ROMs with RetroArch. They work, and fairly smoothly, too. No sound yet and an annoying frame counter in the top right hand side of the screen, but I'm sure that's a matter of the proper settings. (I've been tied up with work lately and haven't yet had the time to sit down for an hour or two and do that.)
However, this now begs the question: why do these games run smoothly when I fire up PCSX ReARMed via RetroArch and not when I do the same directly from Kodi? (I believe that is RetroPlayer, am I right?) What's the difference?
I'm not intimately familiar with the gaming architecture as it is currently implemented, so pardon my ignorance. Is it a matter of tweaking settings in LE or Kodi? I'd prefer to do this from LE if possible rather than having RetroArch terminate Kodi. I can live with it, of course, and if that's what it takes I'll be happy to, but I'm still curious what causes the games to run so badly through RetroPlayer, seeing as it's both PCSX ReARMed doing the actual work here?