Deploying my deplorably rudimentary spreadsheet skills once more, I now have a table cross-referencing the Cliff Edwards transcription discs I know of with the ones I own. Along with a great deal of recent hunting, I've reduced the number of missing titles—songs recorded by Cliff which I don't have in any format—to 54, which is a huge improvement.
Of course, I still have a pile of discs that I'll need to have digitised by a specialist service, and there are some songs I can find but simply not afford, such as the discs I saw on eBay which would cost about £150+ to buy and have shipped… for only one or two short tunes. Still, there are only a couple of discs for which I have no contents list, so if I can find those it may reduce the "missing" list yet again.