Make sure to check the A/C clutch relay, the HVAC relay should be ok since you have power to the blower.
Just find another relay in the fuse block that is similar in color, then check to make sure it has the same part number, and do a swap. I believe the headlamp relay may be the same.
Looking at the connectors, you are correct, they cannot be swapped unless you use a hammer.
I would still be looking very carefully at the black connector. This not only feeds the mode doors but also receives the signal from the EVAP temp sensor, and without that signal, A/C will not come one.
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