Well if your convinced the screw heads are a…screwed then you can take a small pair of pliers and (after) removing the back cover over the electronics yeah screws again try and somewhat hold the jack harness from the back with your fingers and use the pliers to remove the nut on the output jack. Pull the harness out, it will be a pain but can be done, resolder the jack correctly and feed the harness back in (don’t loose the lock washer) and reinstall the jack. Yes a pain but can be done. other little tricks are feed a pipe cleaner from the out side and once in the electric cavity bend it over stick it in the jack and feed it back out so you can put the nut/ washer if there is one back on. Also if you cannot hold the harness to tighten the nut ( you don’t want it spinning as it will rip your wires off) then take the hopefully needle nose pliers and stick them in the jack and hold the tip against the tang or just expand them and hold them open this should give enough tension to tighten the nut. The reason the screws are getting messed up is the screwdriver not the screws get a better or more correct fitting screwdriver lol. In the end remember you can’t brake what’s already broken so at least give it a try. Good luck we’re all counting on you.