I believe they broke down the shaft aways, because they are turning without biting, but they are also not coming out easily. i.e. unscrewing them does not remove them.
I think I can get the top part out with a vise grip, but I would welcome advice on how to deal with the threaded part stuck in the hole. Not sure a typical extractor would get it done.
It would be reasonable to ask why I didn't stop after the first one broke. I don't have a good answer.

Next I'll have to get some decent screws to hold this thing down.