This is one of my little historical asides ... it probably won't help much with the needed repair.
> ... I'm getting a nasty hum in the right channel, which changes in frequency and intensity when I touch the active collette (or any other nearby metal object, like a desk lamp).
"Colette" is a female first name, not a piece of equipment or part thereof. Active accessories (thin, visually unobtrusive extension cables, goosenecks or rigid tubes in which the first stage of the microphone's active electronics are located at the capsule end) were invented and patented by Schoeps. Their "Colette" microphone series, introduced in 1973-74 and still their leading product line, is more technically known as the "CMC" series, and "Colette" is what the third letter in that name stands for (the first two stand for "condenser microphone" using an internationalized, i.e. English and American, spelling).
The name was chosen because for a number of years that were crucial to the company's survival, their largest single customer had been the French radio network--then called ORTF, later renamed Radio France--and Schoeps' main sales contact with that organization, a former Colonel in the French Army, had a favorite niece named Colette.
Looking back now, that may seem like a somewhat peculiar basis for such a choice. But it was up to Dr. Schoeps, and that's the choice he made.
--best regards