If you want to recover the old one at some point try a thinnish drill, very fast. You'll knacker the drill bit but the heat may help loosen it. Then if you use a bigger drill bit, there's a chance you may actually be able to screw it all the way through and out the back.
Worth a try.
Another tip........... this sounds counter-intuitive but sometimes you can crack a bolt by tightening it a tiny bit first.
PS. Don't let anyone every tell you aircraft engineering is all fancy finesse. BF hammers and screwdrivers used as levers all day long. :rofl: