A solution to one part of the project has presented itself: it turns out
that the wardrobe has a slightly recessed back, which means there is just
about enough clearance for a conventional-thickness plug in the existing
socket.

In the apparent absence of surface-mounted sockets with less protrusion than
normal, it looks as if I'll have to go with the smallest available option,
which seems to be a 25mm box and a surface plate as slim as possible.

Thanks to all for the thoughts and advice.