You've given this much more examination than I have thus far. So here's the question, is there room under there for a Turbo040 or PowerCache to fit, if the adapter is miraculous enough? Leaving the PDS slot free, of course.
Both Turbo040 versions? Or only the more modern one which does not have the cache daughter board?
Worst case, we could go to a six or eight layer board if necessary, so that it is no bigger than a 128 pin 13 X 13 socket and Euro-DIN connector. Even worse case, we use surface mount for the CPU socket and put the Euro DIN on the same real estate on the other side of the board. Oops, that isn't going to work. There's no SM version of the Euro DIN connector. Silly me. See what happens when I think out loud...
Or move the adapter board up higher, and mount the Turbo040 on the underside of the adapter, if that will make the geometry work better.
The height is controlled by the sockets, but also by the header pins which go between the sockets, and those headers can be had (or could be had, I'm not very optimistic about their availability these days) in various heights.
Really worst case, use two circuit boards connected by flat flex cable so the Turbo040 need not be sitting right next to the socket, nor in a horizontal orientation. However, this runs the risk of too long connections. Still, 16 MHz gives one a lot of wriggle room, it's slow enough.