So, after a lot of poking, prodding, cajoling and peeking, it appears that ALL the internal WordPress links are already relative, rather than full, links. As a result, it appears that there’s nothing I can do to actually fix this problem. I’m passing it on to local Tech Support (also known as “Mrs. P”) to contact the domain host and ask them to remove the bleeping redirect. I don’t need this site to be SSL and their implementation of the certificate has caused hours of problems for absolutely no benefit whatsoever.
Net result: FAIL.
So I did this.

And this.

Yes, I’m aware that the field boundaries and roads don’t quite line up… I had a choice between making the airfield remains match the historical photograph or making the surrounding area match the historical photograph, so I went for the airfield option. If you take off the old photo, the airfield sits perfectly on the modern day imagery beneath it. Lens effect maybe? Not sure. Whatever. I now need to try and find a Aerodrome Reference Plan or something to place all the buildings, because while they are clearly visible on the old photo, they’re far from identifiable on it, unfortunately.
Or I could just guess!