The post by License is the best post in this thread. I have used the "down pressure with a drill press" a couple of times with success and also the end mill. with the end mill very much care must be exercised to only cut the screw heads off, leaving enough screw shank to grip with pliers after removing base.
Working as an aircraft metalworker, we actually had a screw removal tool, that used this exact principle. It used an adjacent screw hole as an anchor point, and a lever to apply the pressure as you turned the driver bit.
https://b2b.snapon.com/productDetails/883508/2/888783
For the likes of a slot screw head (also works on pretty much any other stripped out screw head) like that, one trick I used to good effect, is to use a Dremel or air pencil grinder, with a carbide dental burr (the bits the Dentist use, to carve your teeth for removing cavities) and carefully make a bigger, uglier, deeper enough, slot. then carry on per normal. Figure the screw is buggered anyway, not a thing to lose if due care is taken not to ruin anything else.
On Impact Drivers, you must insure that the driver is going to turn the correct direction when struck! It is not obvious, and unless you know to check, the CAN be set to provide their magic in either direction. To check, place the driver tip against safe surface and press down hard while watching the rotation of the bit as you press, If the turn is in the wrong direction, you have to flip the driver to the other side of the cam. I find that sticking a Cresent wrench on the drive square works really well.
Likely a bit much for OP's prob. 
