I used my new bits. Trying to be careful not to drill too big at first, the first bit did not "catch" and turn the broken piece out, just cut it like a hot knife thru butter. Stepping up twice more did the same. The final bit I used was a RH one the proper size for use with a 1/4-28 tap. I opened a brand new tap but it is a tapered tap and I need a bottoming tap evidently. The replacement nipple I have is 1/4-28 but I believe the old one was 6mm. My local muzzleloader shop assures me that a 6mm hole can safely be redrilled and tapped to 1/4-28.
Guess I'll be looking for another tap.
On the excessive gap(s), I don't believe moving the barrel/breech back is an option so I'll be looking at filling gap(s) with wood.