The bolts that hold the side panels, bar ends, and battery box are definitely PH03, but most every other cross-head is a JIS (front brake reservoir, carbs, undertail screw, etc, IIRC). The strange thing is, the tool kit Kawi gives you is so crappy that it can't even undo the confirmed Philips screws! It truly is a clusterf**k that can't be solved with one set of tools or the other, which is why replacing with Allen/hex head where possible is such a good suggestion.
I suggest using the drywall bits for the JIS screws/bolts and standard Phillips #03 for most of the rest (PH02 on the reservoir). Replace the JIS screws as you get then out (usually marked with a dot). If you bugger your bar ends with a PH#03, it's because it is soft metal with permanent thread locker that requires heat AND leverage/impact and NOT because it's JIS (it isn't). All the leverage in the world will just tear it up like butter without heat. With heat you may even be able to get it off with a normal screwdriver.