I'm still a bit confused ... when you swap the logic boards, do the respective problems above go with the logic boards? In other words, the SE/30 with no sound always has no sound regardless of the logic board but the video only follow logic board #1? Or does the sound problem go with the logic board as well?
For the sound problem, if the cables are correctly connected, this is almost certainly a failed cap problem, which hints at leakage which may be causing your other problems. If Only in one Mac regardless of logic board, then the problem is on the analogue board and replacing the associated caps will fix your problem.
Some thoughts from Pina on the video. The closest things he describes to this problem are reversed, or bad simms, since your Simms are all the same, reversing them is not the culprit (unless they are of different manufacture). If you have completely switched the RAM SIMMs out of the good logic board and the video problem is still there, then they can be eliminated. However, one thing you say concerns me. In addition to the pinstripe affect, you say there is a fluctuation with each activity. Is this on both Macs, or just one of them? If just one, you have a flyback failure, or other video circuitry coming on that Mac. If both, then this activity is on the logic board as you suspect.
Have you adjusted all your voltages to make sure both Macs are properly powered?
I'm amazed that Pina's books are so thorough yet leaky caps are never mentioned. I can only assume that this problem did not turn up until after the first decade of life for these Macs and Pina's books were all written within the first ten years of the first one sold. The fact that you don't see any evidence of leakage does not mean it's there. After you make absolutely sure you've tried everything easily done to fix the problem, you might seriously consider running it through the dishwasher, as many here have successfully done. If that doesn't fix it, then you're looking at tracking down a bad chip. Which may or may not involve cannibalizing from a known good board, in which case, what's the point? Just get a new logic board.