Don't drill the holes off center!
It would help if you knew the grade of steel you were welding. Standard welding rods and mig wires do not have enough carbon in to harden, so the hardness comes from the carbon and possible alloying with the base metal.
A hardzone is best prevented by preheating the part to about 500 degrees F before immediately welding it. As a further precaution, drill the hole out larger than the tap size and countersink from both sides so you can get down into the hole properly while welding.
Preference might be given to stick welding as it is slower deposit and allows a bit more heat to go into the weld which helps to anneal the weld zone a little bit.