Left hand thread lug nuts on driver side

No, don't drill them out larger.
Drilling the centers will relieve the pressure and gives the outer surface of the stud a place to collapse into.
If it's broken off flush, you mne, that you have to go left hand, two would be enough for me to go all "rights"
Already ordered some right handed studs. Plus then all my lug nuts will match. My guess is the last person that dealt with this couldn't find matching nuts. In fact, I'm glad I broke off the post because they had installed a third style of lug nuts that were too small on one wheel.

So drill out the centers from the inside of the drum, push them out from the inside. Then push the new ones in from the inside?