Heat and torx. Get a torx bit that just barely doesn’t fit and hammer it into the stripped hex bit. Then use a torch or heat gun to warm the whole thing up until it’s just barely smoking. Using finger pressure, slightly more then gently, twist cc on the stripped screw as you heat it.
Little heat- gently try it - little more heat - gently try. Once it loosens up a smidge it will feel like it’s stuck in glue - it is - keep gentle pressure and hit it with some more heat
The heat won’t hurt anything on the shaft or pinyon but can hurt some things around it like wire, paint, deck if you’re not careful. Aluminum foil is a great shield for things you cant get out of the path of the torch/heat gun
With a dremel make a cut here and heat up with a heat gun and using a flat heat screw driver take it out.
To add on to this advice, of the two options I’ve had a better experience with a butane torch than a heat gun in this scenario - usually torch it for about 30-60 seconds and it breaks down the loctite really well.
I don’t want to criticize you, but looking at this photo, I suggest replacing all the screws in the board. 
I agree
With anything but Philips head
These are all excellent suggestions, I have another if the others don’t suffice and definitely ditch those Philips screws.
Heat the pulley with a gas torch just the right amount. Remove the pulley with some screwdrivers and other blunt objects by levering, or better yet - a small gear puller if you can get one in there safely. Just because the screws there, doesn’t mean the gear won’t pull off with enough gusto.
If you get the pulley off, heat it some more, and drill the grub screw. If the drill bites, it’ll wind itself in and come out the other side.
Also, I don’t understand. How is the screw already poking out?
If all those suggestions above fail, just use a dremel and cut the pulley off and replace it