In addition I had automated searches running on e Bay for these 14 amp types - whenever one appeared for sale I would contact the seller, asking for the serial number.
9 out of 10 did - many thanks to them for their trouble and good will.
A little light Googling revealed serial numbers for a few other amps in the range - they seemed all mixed up together.
Then the terrible truth dawned on me: they WERE all mixed up; Fender had decided to change their 35-year-old system of serial numbering so that, starting in 1982, every amp had a unique number.
I would have to collect data for ALL the amp types, just to work out how many were made of mine.
Then I became aware of the amazing work Greg Gagliano had been doing since the 1990s - the summary of his latest results are here - and that his research stopped just before the Rivera-era. However for this range of amps at least, I reckon it's not just a policy of withholding company-confidential information. It's no criticism of Fender to suggest that they were too busy making great amps to keep records just so some amateur can use them thirty years later.
While it's anyone's guess how many of these were Champ II and how many were Bassman 20, they seem to come up on e Bay equally often. People keep on referring to this 'fewer than 500' thing, especially when they're trying to sell one as 'rare', but I'm still waiting for anyone to point back to the original 'fact' of the matter!