Stan, I'm no expert on this but I do have experience.
My old G4 is the same one as yours and is running OS 9.2.as- high-as-it-was-possible-to-go. It works perfectly well because I don't mess with it, ever. I eventually bought an iMac OSX because the G4 OS9 was upgraded both hardware and software as far as it was possible to go (including extra RAM from Crucial). All internet browser development for Mac OS9 stopped and the last one, IE, became ridiculously unworkable, so, a new iMac it had to be.
On a previous Mac I partitioned the disk (to run some MS apps) and regretted it from then onwards. I'm always wary of partitioning disks because I think the only way back, to unpartition it, is to wipe the disk completely. Hope you have a good back-up regime!
I don't think you can drag OS9 items to the OSX partition but I could be wrong. Jon or Tacit would know. I also don't think your new monitor has anything to do with it, since it's mouse inactivity you report.
I don't know if any of that will help, but at least here's someone who has been there before you and eventually had to stop doing that and buy new kit.
Best wishes
