Nano-surgery.
There was a tiny bit of the screw sticking out of the front side, but not enough to get Vise-Grips on it.
So hello Dremel. I got a grinding bit centered in the backside, so I should be able to get enough bored out without touching the threads. Getting the screw remnants out will be tricky, so I can use the screws that BF sent...
Cross yer fingers (and cross yer eyes, teeth, cross yer hair, piggies...

)