I emailed a friend of mine back in So Cal about this, and he gave me another option, one I didn't think about. He said from what I told him about the wiring diagram for the relay and the relay socket, they're both wrong. He then told me which wire should be going to which function off each terminal on the relay, and they didn't match the diagrams on the parts boxes at all!

So after work today, I'm going to disconnect all the wires coming off the relay socket, look at the relay terminal numbers, find the associated wire, then route it accordingly, ignoring the box-supplied diagram. Maybe that will get this thing to work...

Guess I could've made a faulty assumption in thinking that the wiring diagrams on the back of the boxes were actually correct...