Ouch!
Before resorting to drilling, I would start by blunting the tip of a Phillips P0 driver so only the upper part of its flutes better engage what remains of the flutes in the screw head. There may be enough there to get some purchase.
Phillips, Posidriv, and Frearson screws look rather alike from the outside, but the taper of their bits' point can be different. PosiDrive and Frearson bits are blunter.
That is a common cause of stripped screws. A Phillips bit bottoms out in screws intended or the other drivers before making full contact with the flutes. That is why shortening of a Phillips bit make work. Early in my computer abusing career I encountered the taper problem and have kept a modified P0 drive in my computer whacking kit ever since.
That failing, you can't use heat because the part the screw secures is plastic. Sometimes you can wedge an Allen wrench into a hole like that Give the wrench a LIGHT tap or two to seat it and then use slow force on the wrench.