Tms, I did everything you said. Used a whole can of brake cleaner, switched to my Kobalt 6-point sockets, and put the socket onto the plug, then attached the breaker.
Plus I removed the alternator mounting bolt, had the engine tipped forward, and I was standing on top of my engine, while picturing the socket slipping and me faceplanting into the stb bar and knocking out my teeth.
No hard hits on it, just slow brute force, I did 3 rotations with the breaker.
But as soon as it "broke", it came off super easy.