Kevin at Lynx Innovation kindly organised to have my EVD5 Backplane design made. I've stuffed half the components and tested out a few channels and it looks like I didn't stuff anything up too badly. The biggest mistake I made was to specify the wrong hole size for the main header where the EVD5 board plugs in (the rows of white sockets). This is somewhat inconveniently fixed by drilling the holes bigger and then soldering the top and bottom. Drilling the holes bigger destroys the plating on the inside and disconnects the two layers, so you have to solder the top and the bottom separately.
There are a couple of places where I could move traces to increase separation (and reduce the chance of shorts) but otherwise, I'm very pleased. Now all I need to do is order the enclosures and find some elves to assemble everything.