exterior mirror's mounting screws welded shut

[awitate]

So I wanted to install the original looking mirrors on my 63. Guess what? I found where the screws are suppose to go (under 1/4 inch of bondo) but the kicker is the screws are permanently welded onto the plate. The method they used was basically to hammer the screws deeper into the door, then weld, then bondo. Since it was a big mess(can't see the screw heads) I drilled in to see if i was in the right spot which i was but what do I do now? can I try to drill the screws out? the heads won't come off will they? That first hole is not centered and I probably won't be able to center the remaining 5 so is re-tapping out of the question?