First try to heat the screw area up a bit to melt the glue or epoxy. Don't heat it too much though, because if you can melt the adhesive holding the screw in place, you can also melt the epoxy holding your skis together. If that doesn't work, try to grind the tip of a #3 Phillips down a bit so you make sure you are getting maximum contact area / torque on the screw head before it slips. If neither of those methods work, use a dremel to cut a slot in the screw head so you can get it out with a flat head. Or you can also use a screw extractor.

I've has similar issues. Around :50 seconds they tell you to drill a hole deeper into the screw so the bit can grab onto it. This has solved my issues 100% of the time. However, after you drill into it you may need to use a wider phillips head screwdriver because it makes it bigger (like a number 4).

Putting a rubber band on the tip of a philips head can help. Vice grips also work wonders if you can get them on there.

Manual impact driver and a hammer.

Get a left handed drill bit, basically a drill bit is threaded the opposite so as it spins it pull the bolt out