I got it out. I tried several methods most of which didn't work.
Ultimately, hitting the NDS crank-arm with a rubber mallet was enough to loosen it a hair. Once it moved 0.5mm or so, I was able to use a breaker bar and the self-extractor to finish it.
So follow-up question.
I bought the bike used, and the plastic thread protector for the Shimano tool is missing. Does anyone have a recommendation for something to put in there to keep the threads clean?