The MIG might be the best way, but one other thought if a socket won't
work, take a shaft collar and bore it on the lathe to fit tightly over
whats left of the head, then tighten the setscrew(s) on the collar on
the head of the plug. You might even consider machining a slight
counter bore on the end of the collar to grab the OD of the plug
flange. Then grab the collar with a pipe wrench or have a nut welded
to it. I've used the TIG/MIG method on several occasions with good
success, but not on a drain plug. Be careful while you are welding, if
the nylon washer melts before you stop the arc, you will have a fire
from oil leaking out and then a much bigger problem...