Just a thread resolution post:
I opted for the Walton tap extractor. After soaking with penetrating oil, I got the broken piece out, but it didn’t come out without a fight! Almost took out the extractor fingers.
I suspect the first tap broke because I drilled the hole right between two splines, but not all the way through, and it was stuck between a rock and a hard place. Oh yeah, and because Mr. Gorilla Hands. Bad combo.
After removal, I drilled out the offending stubs, got a new tap, and finished the job.
For future reference though a 211121X Spicer seal has the zerk in it.
Admittedly, that would’ve been much easier, but that is what I have on the rear driveshaft and I have damaged the grease fitting from rock contact before. I think the fitting will be safer hiding behind the yoke, at least on the front shaft.
Thanks for the help everyone!