After more testing, I've definitely narrowed the problem down to the hard drive.  I booted to a 6.0.8 floppy (actually, a 6.0.8 image on my shiny new floppy emu!) and then played a bit of Crystal Quest (the app was located on the hard drive, not the floppy).  Rock solid throughout.  I quit out (after getting to level 27   , let it sit for 15 minutes with no screen saver, came back, and things were still fine--right up to the moment I double-clicked the hard drive in the finder, when it immediately crashed.

I'm pretty certain now that the problem is the hard drive, and not only that, the crashes only happen after the machine has been idle for a bit.  My theory is the drive has some kind of sleep/idle state that it kicks into when not busy and then the Mac doesn't know how to wake it again and crashes.  Has anyone seen this before?  Is this a common feature of later SCSI hard drives?

Meanwhile, I'm hoping a workaround may be to just set a very short screen saver time and hope that's enough to keep it entertained in the event I take a phone call while using the Mac.  I'm also looking forward to trying the hd20 firmware for the floppy emu, which could also be a solution (though I'd prefer a working internal drive).