Test with both vanilla and eventlet stdlib

We intend this project's code to function both with and without
eventlet monkey patching, so we should test that way too.  This adds
a separate test run that explicitly enables eventlet and removes
the racy monkey patching that existed before.

I left the eventlet-specific unit test because it's making direct
calls into eventlet, so it is a somewhat different case from
implicitly using monkey patched classes and I'd rather leave a
redundant test than remove it and find out it covered something
the others don't.

Change-Id: Idbe9cdd90e9ce5e38b03ec1c20066928daa9ef00
Closes-Bug: 1367966