First off, buy yourself an impact driver:
About $20-$50 and try to avoid the cheap chinese knock offs. Spend money on a good name brand.
If you can get at it a vise grip on the head of it or cutting a slot in the head with a Dremel or a hacksaw works for a stripped Philips head.
The worst problems are when the head is stripped down in a deep hole like the stator where you cannot get a hacksaw or dremel on it.
That is when I get out the nut extractor. Made for stripped nuts, they will also work on bolts and screw heads:
I have a set of these, they are THE BOMB. Again, buy a name brand set.
Now is even these won't do it, and the part comes apart along the same axis as the bolts, I
drill the head of the bolt off with a slightly larger drill than the shank.
So if it a 6mm bolt like holds the case halves, I use a 6.5mm or 7mm drill or SAE equivalent.
So, to remove a tough Philips screw in a tough location, here are my steps:
1) Impact driver, whether stripped or not, I loosen all the bolts with the impact driver.
2) No go? Heat. Propane or MAPP gas to the head of the bolt, penetrating oil, impact driver again.
3) Stripped? Vise grips, cut a slot, or nut extractor.
4)Cannot get access? Put a nut over the screw head and MIG weld it to the screw, penetrating oil, socket.
5) No room or no go,
drill the head of the screw off, pull apart and remove screw shank with heat and oil and vise grips.
6) REPLACE ALL PHILIPS WITH HEX or ALLEN HEAD SOCKET SCREWS!