David,
I haven't read all your posts, and haven't drawn a wiring diagram, but the fact that in the last picture you posted (pic 7) the old and the new stacked connector are still connected to the old, faulty relay may be creating havoc. Have you tried it without the old relay in the circuit (i.e. just unhook the old and the new stacked connector from the old relay).
Otherwise, trace all the wires and draw the diagram, it should tell you if it's correct.
Testing a relay is VERY easy. Disconnect all of the relay completely. Connect an Ohm meter to pin 87 and 30 of the suspect relay (it should show infinite resistance), and then connect 12V across 85 and 86. The resistance on the Ohm meter should drop to 0 if the relay works.
Peter