You'll only get one quality shot at getting those screws out, after that it will be damage control.
First, I'd use a flat-tip punch and small hammer to flatten the areas where the Philips slots are starting to deform. Yours aren't too bad, you should be able to bring them back to full functionality several times if needed, then toss them after they're out.
To loosen the threads' grip on the case metal (all of mine have had oxidation on both screw and threads), I'd suggest applying some serious heat to the screws IF you can do so without putting the coils at risk. If it were me, I'd protect the coils with sheet metal while applying heat with a small heat gun, or if you haven't got one, a torch on low heat if you're comfortable with that. The idea is to get the screw nice and hot (maybe 160F to 250F), then let it cool down and try removing it (one or two tries only, then heat it again and use the punch again if necessary). It's also really important to use a Philips impact tip that
exactly matches the screws, or is even slightly bigger than ideal; a too-small one will spuzz it right out and you'll end up with a rivet.
![Sad :(](./images/smilies/icon_sad.gif)
Be sure to push down
hard on that impact driver and use short bursts, obviously.
Using the above techniques I recently removed two butter-soft Allen screws which were Loc-Tited really tight into a small cast-aluminum brake cylinder. I used my handheld impact driver and hammer as I thought the 120V one was too much. It took 3 heat applications, probably 4 or 5 goes with the punch per screw, and a whole lot of medium-hard hammering and twisting, but they came out without damage to the cylinder or mount.
Ray