I tried the blue wrench and a new straight flute extractor. In return, I was rewarded with zero progress. It continued stripping the fitting.
I dug around in my plumbing stash and found a spare fitting. It has 1/8 NPT threads. I grabbed my tap and drill bits and went back into the shop.
Dropping the crossmember and resting the oil pan on the steering linkage helped. I was able to shove it off to one side just far enough to work the drill into position.
After some careful reaming and holding my tongue just right I was able to get the hole tapped again. It put up a fight and I had to go fairly slow. The tap was breaking up the remnants of the brass fitting.
I also pulled the cooler line off the car and cleared the threads on it to get rid of all the stripped brass.
That's where it sits right now. Everything will fit back together. I simply need to reassemble the cooler line then put the transmission back in place.

Progress, but a PITA.