I gave it my best shot and ... it worked.
First I put the connector in an ultrasonic bath, to very little effect.
Then I replaced the water with warm IPA (yes, I'm aware of the dangers; I took appropriate precautions). Again, not very much action.
Finally I made up a strong, warm solution of citric acid and put that in the ultrasonic cleaner. Voila - it cleaned most of the corrosion off.
The last steps were a good rinse in plain water and a final slosh of IPA. The plating on the pins has clearly had it (but I can re-plate); the most important thing is that it works well enough for now and I have the use of my test instrument, at least for a while. Given that I didn't use it in the last ten years and only have one job for it at the moment, that's good enough.
Thanks for all the help, everyone.