Genghis,
From your original post:
This was a bit of an irritant when already working fairly hard single-pilot IFR in IMC, in fairly crowded airspace, and preceded by no warning.
Not sure about your experience or qualifications, but the circumstances which caused you to start this thread could well have been the first hole in the Swiss cheese leading to a loss of situational awareness incident. There are some red herring posts on here which get bogged down in the esoteric technicalities of the various types of service, and which don't really address your concerns. When I was controlling I tried not to forget that ATC is a 'service'. In Class G airspace in situations like yours, I would always give the pilot a bit of useful information about the onward situation, with a phrase like 'Shortly leaving my area, no known (or observed) traffic in your vicinity, Squawk 7000 and free-call XXX'. If I knew of, or could see a busy area a little way ahead, but out of my area, I would pass this information and suggest an early call to the next unit. I know that seriously busy units may not have time to add those half dozen extra words, but controllers should also be aware that just dumping a (possibly very inexperienced) private pilot could lead to confusion and possibly panic in the cockpit.