This happened to me not so long ago. Same situation. I had the left hand drill bit on hand. One tap with a center punch and put the bit in and it backed it right out, slicker than snot!! I would try the left twist bit before going the easy out route. Good luck.
1996 K2500 Suburban
Second owner, Former Fire Dept Vehicle
"F" Engine, 4:10's looking for 3:73's
D-TECH Remote mounted PMD, HO water pump
1998 air box with K&N filter
Fluidampr
17" GMC Alloy Wheels with 265 70 R17's
RACOR 490 fuel filter with heater and 2 Micron Filter