I've got enough Macs and monitors that I probably won't worry about trying to make the Sawtooth work with the 23" but I'll keep it in mind.
Going back to the PowerBook 165 I mentioned above, I managed to find another very cheap one that turned on with a chime and displayed a blank white screen. I was sort of hoping that the seller just didn't know how to adjust the brightness and contrast and it was actually okay. I did ask them if it had been opened, hoping that it might have a usable hard disk in it. Once it arrived, I found that it didn't do anything but display the white screen, and while there was a hard disk inside, there was no sign of activity from it. It does boot from the boot floppy I made, but there is nothing on the screen.
I tried swapping various parts around between my two machines, but was never able to get the screen on the new one to do anything, so I'm guessing it's something wrong with the screen (I tried swapping everything including the board that controls brightness and contrast, but it didn't seem to make a difference. I did apparently solve the issue of the machine restarting when touching the top trackpad button (which I assume was just are result of something shorting somewhere). But no luck with the screen or hard disk, so I'm not much farther along than when I started, although I can pick and choose the components that are the in best shape and make one unit out of them. I do have a new appreciation for how modular these computers were. It's really quite impressive how easy it is to take them apart and swap components.
By the way, my old 165 had a modem card in it and the new one didn't. I didn't realize that was optional.