When you "Drilled it out" do you mean you used a bit larger than the head of the screw and shaved the screw head off, or do you mean, you drilled into the screw hoping to drill the screw out from the hole?
If you used the large bit method then you should be able to pull the plastics off of the new stub of a screw then grab the tip with a pair of visegrips and remove the screw by manually unscrewing it with the grips.
I am played this game with 3 screws on a 1985 LT250R motor over the weekend, I was able to remove all threee by drilling the tops off.