Turned out that my old Apple CD 300 (the cartridge style one) was way, way, way too slow for some games, including Myst. At 2x, it's pretty terrible.
However, for anyone interested, it was trivial to yank the drive and install a different SCSI CD-ROM I found on eBay. Keep in mind that for older 68k Macs like my IIci and the entire compact line, the SCSI bus is
really freaking slow, so any drive over 12x is unlikely to make more of a difference than a 12x drive. Once you install the drive, do
this resedit hack on the Apple CD-ROM system extension so that the OS can use your new drive.
It was definitely worth the $14 for the drive and the two hours I spent fixing it (turns out one of the little plastic gears that handles the tray loading mechanism was cracked...whoops).