I came across this gem, which seemed to be close to what I wanted. However, I want to use the already-written controllers from a referenced assembly.
My first crack was to reference the assembly, set up the routing rules the same as the original webAPI project and go, but I get 400s every time I try to call the self-hosted service. I've picked through the innards of the request with Fiddler, and aside from the address differences, the requests against the webAPI project and the self-hosted project are identical.
I feel like this ought to be relatively straightforward, but I haven't found an acceptable answer.