After visiting a hardware store, a flat:
The offender is in the upper left corner.
Some sort of sheet metal screw based upon the head:
Using a flat, get it high enough to grasp the head:
Needle nose, vice grips make it easy to unscrew:
More easily than trying to remove with the flat screw driver:
Here is the little bugger. The flat head allows it to rest in the parking lot, pointy end up:
Unfortunately, no space to work on the repair. So a handy biological (pine needle) went in the tire so the car could back up enough to work on it. I probably should have just backed up with the original object to make it easier to take out:
So here is the plug in the 'needle' tool to insert. The infernal needle tool:
Covered in adhesive, it made an impressive wad and would not go in the tire. I briefly thought of backing up over the tool to force it in ... but came up with another approach.
I had 'rasped' the hole larger but decided to try a flat screw driver:
It appears to have worked. The wide-side of the flat screw driver avoids clumping up the plug at the entrance of the hole. I am thinking about getting a similar flat and grinding it in about 1-2 mm with very narrow shoulders. The wider surface area will avoid the clumping.
So I put a plastic bag over the external, patch wadding, and backed over it:
Now to go test it.