Looking at the damaged screw, I'd probably cut an entirely new screw slot on the head.
Make it 90* from the damaged orig. Though the area on the right side looks very damaged as well, a new slot would take advantage of the yet undamaged metal on that side where the CCW
effort of the screw driver bit will push against.
A simple Graver chisel with a flat point and a very high Heel on it. That will allow the graver to get down into the slot as it's cut and not have the back edge of the shank of the graver dig into the countersink in the plate causeing further damage.
A simple flat edge/point graver can be made from a lot of things. A file with a thin thickness to begin with is one.
Grind the thickness further if needed to the width you want for the slot to be cut.
Put a flat bottom on the piece, then grind or stone the point to about a 45* angle. Anything more will tend to not want to cut too well after you do the next sharpening and that is to put a Heel on the bottom flat of the graver.
Simply put the now sharpened point graver on the bottom flat at the point on a stone .
Drag it backwards and it will stone a small flat on the bottom at the point. That is the graver's heel.
It doesn't need to be long. It only changes the angle at which the graver needs to be held to start cutting.
It also adds strength the sharp point on the graver
The higher you hold the graver above the stone, the more severe the heel angle will be.
If you stone a heel that ends up giving you an included angle betw the heel and the point that is close to 90*,,leave the heel and resharpen the point angle itself to a 'sharper' point.
It won't hardly cut at all if the included angle is 90 or very near it.
In normal cutting/engraving the heel is around 15* lift. Works well a lot of engraving. Most all engravers have a special spec they like. But in this instance
For this you want the heel to be more,,45* and more is OK.
That makes you lift the graver handle higher before the point actually begins to cut into the metal.
A high heel on a graver is used when cutting work down on a piece such as the inside/bottom of a bowl. Same idea, you don't want to nick up the high edges of the bowl with the shank of the graver.
That is what you want in this instance so the back edge of the graver doesn't touch the counterbore in the plate as you cut.
The high heel will make smooth cutting a bit more difficult than the lower angle(s). But you are not doing any scroll work in there ! It's just to chisel out a new slot.
It doesn't have to be pretty, just make it a deep as you dare and keep the sides of the slot straight up for the screw driver bit to push against.
Grind a new screwdriver bit to fit the new slot as tight as possible.
Then back to the drillpress or mill.
When all else fails, drill it out and pick the pieces out of the threaded hole. Make a new screw.
If you do get the mangled screw out and the threaded portion is still good, You can use it to make a new screw.
Turn or file the damaged head off of the screw. Down only as far as it will leave a 'cap' of the old head dia on the threaded shank.
Then silver braze a new head into place. Soft solder won't do even the newer greenie tin/silver stuff.
Turn or carefully file the new head extension to the same dia as the 'cap' that was left on the shank.
Leave the new head taller than needed and put a quick hacksaw screw slot in it. Doesn't matter where the hack slot is.
Use Color the new head with Sharpie or similar marking 'dye'.
Screw the thing into place , running it in back and forth a few times to seat it all the way. Then scribe a ring around the new head where it sit's level with the plate AND scribe a small 12 & 6 position on the extended head at the same time.
Remove the screw and now scribe those 12&6 positions down onto the head that will be below the surface. File off the extended head material till you are near the circumferance scribed line.
Don't go all the way to the line.
Move the 12&6 marks remaining on the head to the top of the screw head.
That will be your indicators for the new slot.
I use a Jewelers saw and .020 width blades for these type to cut the slot. A hacksaw blade with the set ground from the sides will do as well.
When you go to cut the slot,,back the cut up CCW from the 12&6 scribed marks to about 11 & 5 positions.
That will give you some extra effort in tightening it down when installing it for the final time(s!).
If you don't do this last little thing the screw will most often go in and tighten a little past 12& 6.
Now carefully trim the head level with the plate
I need more coffee now..
