Just a general note about capacitance, which may not be all that helpful
When testing whether power is any good, you should put the voltmeter on AC and check the voltage at the chip power supply pins. If the power is good and filtered, you'll see little to no reading on the meter. When electrolytic capacitors begin to fail, they will begin to leech at the power supply's capabilities, and that will be evident with ripple voltage.
I've only recently heard about the SGM (basically since I started browsing this board), so I have no idea what its internals look like, so hopefully I don't come off as sounding like I know everything in the following points. I also can't guarantee complete accuracy, only having an associates degree in electronics troubleshooting from the local community college--obviously I'm only vaguely aware of design issues and not an authority on how to mitigate signal integrity issues. Now, disclaimer aside:
Even if all of your caps are good, there could even be a design flaw in the SGM itself that makes it vulnerable to odd situations such as static electricity, certain bit patterns, phase of the moon, etc. At its core, a capacitor is just two metal plates in proximity that are not touching. Well, board traces match that description too. There will be some crosstalk between traces, and if it's bad enough, your signal degrades. So running traces in high-frequency applications can be as much black magic as it is science. If the SGM employs high-frequency components such as an on-board microprocessor, that's a definite concern. At Colecovision's 3.58MHz, you're still pretty safe from that. But at 50MHz or better, that's in the fun zone.
It could be that if you left the board as dirty as was shipped, the game would have worked. The accumulated corrosion could have been fortuitous in providing just enough resistance to maintain adequate signal quality, and cleaning is actually what did it in. As that affects the SGM, perhaps adding a few low-ohm resistors on the signal lines would be enough to fix its issues.
It could well be that the cleanness of the CV board may be the deciding factor in what works vs what doesn't.
But again, just spitballing here.