Latest update: I've had a couple of leisurely email exchanges with Jeff Galin at Electronic Service Labs in Connecticut. Apparently there were three or more "generations" of Dragon transports, and going strictly by its serial number, my deck isn't one of the more recent versions that they typically work on (or perhaps, that they can work on at all--I don't know).
However, my deck was repaired rather extensively by Nakamichi back when they still serviced such things. Did they update the transport in the process? I can't determine that on my own; the diagnostic question that Jeff asked was, "Can you measure the diameter of the right capstan, accurately? It's between 2.4 & 2.8 mm." Unfortunately I can't do that.
So (since I live in NYC) I mused about getting onto a train and bringing the deck to him to look at. His reply was, "If you want to come, please make an appointment." But also: "Although a Dragon overhaul could cost $2475 to $2975, this is assuming that it has at least a 2nd generation transport."
That's a rather dismal state of affairs in my opinion. Not entirely surprising, but certainly not what I was hoping to hear.
P.S.: I just wrote to "Pro Digital Inc." ... just three hours away via Amtrak ...