That receiver looks odd, I hope it wasn't in a fire or something like that.
Anyway, the answer is to give the job to a gunsmith or, if you know of a good one, a machine shop. It requires a sold drill press or milling machine set up to keep the drill from wandering, plus a stiff starter drill. Once the old screw is drilled out, the hole can be cleaned up with a 6x48 tap. That is a non-standard size used in the gun industry, so a machine shop may not have the tap, though a gunsmith certainly will.
You can get new screws from the gunsmith or from Brownells.