Repair tips for stripped screw

Hey all,
I'm trying to repair the gimmick on one of my Action Master Elites. However, one of the screws has been completely stripped, as seen in the picture.
Since it's set really deep, nearly at 1cm, screw removal tools won't reach it. Also the opening is too narrow for a bigger screwdriver, and the screw has never been removed so it's stuck hard. Can anyone give me some ideas on how to get it out? (Preferably without referring to its unfortunate placement... XD)
I'm trying to repair the gimmick on one of my Action Master Elites. However, one of the screws has been completely stripped, as seen in the picture.
Since it's set really deep, nearly at 1cm, screw removal tools won't reach it. Also the opening is too narrow for a bigger screwdriver, and the screw has never been removed so it's stuck hard. Can anyone give me some ideas on how to get it out? (Preferably without referring to its unfortunate placement... XD)