The photo helps a lot Carl.
First the bad news... the damage is worst in the places where the screwdriver bit needs to apply counterclockwise torque, so it will be very hard to apply enough downward pressure to get a good purchase on what is left of the slot. Also, it is recessed deep enough that attempting to cut the slot deeper with a Dremel cut-off wheel would be impossible without doing further damage to the surrounding metal. So I like Mike's idea of carefully grinding a small graver to cut the existing slot a bit deeper.
The good news is that while it appears there is some rusting, it isn't a total loss like a gun that has been stored in a barn or chicken coop. There is always a bit of clearance between male and female threads. And rust occupies more volume than steel, so it tends to fill up those tiny clearances. Rust is abrasive, and greatly increases the amount of force needed to turn the screw. That's why long soaks with penetrating oil are important. Rust, or ferric oxide is also hygroscopic, meaning it draws in moisture, which leads to further rusting. So applying heat with a soldering iron or the heated rod or screwdriver blade as Kutter suggested drives off that moisture, increasing the chance that your penetrating oil can wick its' way deeper into the rusty threads. It often helps to alternately apply heat, vibration, and then hit it with more penetrating oil.
That all takes some time... could be 6 hours, 6 days, or 6 months. Most people aren't that patient, and will end up drilling it out and retapping for a larger diameter screw. I don't see any fresh shiny metal, so it appears you haven't gotten impatient and made matters worse. It helps to have some other projects to work on while waiting for these methods to finally work. My big disappointment with Kroil was that I noticed it often failed to penetrate down more than a couple threads, even when I let it soak for days with fasteners that weren't severely corroded or rusted. You will notice that some penetrating oils evaporate quickly, and will need frequent reapplication. ZEP 45 is one that does this, but it seems to work well if you keep at it. Same thing with the mixture of ATF and acetone, because the acetone is volatile and evaporates quickly leaving the more viscous ATF behind. So it may help to make a dam of clay or silicone caulk to contain a little bit, and then cover it with Saran Wrap.
There have been some past Threads here dealing with penetrating oils and screw extraction. The Burlite I mentioned earlier is made and sold by another member here (docbill), who gave us some good information on what it takes for a penetrating oil to work well. I'm not a lubrication engineer, but decades of using dozens of different brands has taught me they are not all the same.
