Sorry guys, I've been off gobbling codeine and sleeping and trying not to cough ...
I couldn't post the image because it would have meant posting the whole page to get the picture, and I think that's not permitted for copyright reasons. But have a look.
The baptisms spread over the period from September 1801 to April 1802.
They accounted for
all baptisms during that period.
Up to Sept 1801 and after April 1802, there were baptisms at frequent intervals, and all baptisms were recorded in the regular way, with parents' names.
So unfortunately, neither the foundlings nor the adults hypothesis really works, since the baptisms were at different times over several months, and no "normal" baptisms (children of married parents with parents' names shown) were recorded during that period.
It does possibly look like they were all entered at the same time, even though they took place at different times over several months. So I do suspect the names were transferred from some other record, or just entered after the fact for some other reason.
Bishop's transcripts ... I'm not very familiar with them. Sometimes the OPC site has duplicates for events, one from the parish register and one from the BTs. Is there a way to look at them?
Thanks for all the ideas! And now I'm taking my cough back to the chesterfield under some blankies and cats, to watch the Olympic opening ceremony.