Odds are that it's not the seat causing the problem, and there's nothing you cab do to to refinish the needle itself. Your only hope is that it's dirty or dried out. Soak the needle in gasoline overnight, then reassemble it and see what happens. You also need to inspect and check the adjustment on that fuel screw. Having the pilot clear will do little good if the fuel can't get past the screw. You can't say you've cleaned the carb thoroughly unless you do that.