Get an assortment of screwdrivers to find the one that is tight and fits full. It myust fit tight with no play. I found a long handled Kobalt from the Depot or Lowes that is the ticket. Then grip the handle with both hands and lean down on the end of the handle and your two hand wrap like you are doing pushups, with all your weight on your chest and handle positioned there. Then it won't slip. Use your whole upper body to turn screw, not your hands.
When it moves a littte, go back and forth mant times, then take some more, then go back and forth some more, etc. Get some oil under it.
In any case, if the screwdriver slips and ruins the top of the screw, use a new pair of vice grips and clamp down very hard, and do the same as above.
The SS screw is much stronger than the 1/8 alum, no way head will go as long as you don't drill head guts out.
I have no idea how you are going to get the broken screw out, I would if all gas was out and no chance of explosion.
Good luck.