http_test.go

The clients already support it (via the default net/http.Transport),
and it can be enabled with a configuration parameter. The default is
still currently disabled, though there is plan to flip it later to
enabled-by-default if it proves to be working as expected in
production.

We also introduce, via a slight refactoring of the Serve() code, a
test of the top-level http.Handler (with the full middleware stack).