I have no idea what you're doing, or anything about what you might need to make it work. I am curious about... you say "of my 5 remaining working", which makes me think you have others that are not working. Then of those 5, apparently... none of them work correctly, or at the very least, some work right and some don't, because they work differently. My first thought was... "Your 5 remaining working SSM2044's do not work."
Then I looked for a datasheet, and at least got a general idea of what the thing is and does. I've used quite a few SSM parts, when they were Burr Brown, and now Analog, but I had never heard of the SSM2044, because apparently that part didn't make it through the acquisition chain. So it's a VCF, loads of fun, and they are apparently available from a modern second source as the SSI2144, for about $5 each.
Testing the chip, with all those special-purpose pins, seems like the kind of thing where the application circuit is the test circuit. If it works in it's natural home, it works. Otherwise, no. I can't imagine a sort of resistance check or something that would establish the functionality of the chip, though stranger things have happened. The thing is... at the pins, you only get to see the things connected to the pins, with maybe additional random influences upon those things, but there are plenty of bits in there that isolate the circuitry from the pins, so you can't really see what's up deep inside there. Or so it seems to me. And building a test harness would look an awful lot like building a synth module, so... why not use a synth module?
So I would assume, if I was getting funny waveforms with them in place, they are broken, though I would probably look at the input as well as the output to confirm that conclusion. Or the chip-swapping thing does seem good, too. If you have another stash of completely broken ones, you could put these partially broken ones in there with them, with labels that say "broken entirely" and "broken partially".
Then, after concluding they're all broken, I would save my money by not eating lunch for a couple of days, and try to buy some brand new ones that work right, and then move on to making music. Or something like that. So... testing in place, go/no-go result, and $get some new ones. I suppose there is a supply of also-partially-broken ones on the auction site, or chips that are nothing like these that have been relabeled by people trying to make a living under difficult circumstances, but all that seems dicey and unwise if new real ones are available for $5 each.