Really, the best solution is for more Americans to ask for Robertson or Torx drive screws so that your hardware stores start carrying them. Here in Canada, hardware stores carry very few Phillips or slot drive screws because everyone buys Robertson.

So far as the stripped Phillips head screw goes, I'd try:

1. jamming a small slot screw driver into the drive and try turning it that way.

2. If you have good access to the head, another thing to try would be to grab onto the head with a pair of side cutters hard enough to leave an impression and try to twist the screw out that way.

3. And, if push comes to shove, drill the head off and twist out what's left with a pair of vice grips.

In my experience, trying to grind a slot in it with a Dremel usually doesn't work out. That's because often the slot isn't in the middle, and when you twist with the slot screw driver, you often end up breaking off the smaller part of the head.