I'm working on a 1998 Honda Nighthawk to keep me calm in retirement. The person I bought it from had tried to do something with the carbs and destroyed the head of a slow jet. It's a mess. I've tried spraying it with PB Blaster and letting it sit overnight but still can't get it out. I thought about trying to use a screw extractor but not sure if it will work. Any suggestions?

'06 America, Raask foot controls, the bike use to be Graphite and Silver, now its Red and Black.