Yes, the problems traveled with the logic boards. The swapping I did was to see whether the problem was on the logic board or the analog board; and since the problems traveled with the logic boards, that answered that. The logic board with pinstriped video always has pinstriped video, and the logic board with no sound always has no sound.

I didn't even think about the possibility of one of the SIMMS being bad; tonight I will try swapping the RAM between the two units, and see if that makes any changes to how the problem manifests itself. All eight in the pinstriped system are identical, and all four in the no-sound system are identical (but of different manufacture than the ones in the other system).

As for the fluctuation:

When I first got it, each pinstripe was one column wide, and the column to the right of each "dead" column would flicker in and out of life. However, after cleaning the board, it seems to have settled into both columns being dead (as pictured). It is no longer flickering.

One thing I should note is that other than the pinstripes, the system is "working" properly. It boots all the way into Mac OS, and I can use everything normally. As you can see in the screenshot, I've got the "About This Mac" window open, which is reporting 8MB RAM.