You can also use a threaded bolt and a stop washer in the cut to slowly screw the kickstarter "open." Hard to describe but hope you get the idea.
- OR -
Use the screwdriver driven towards the spline and when fully home, put some paper towels between the kickstarter and gearbox cover, then spray the splines with PB Blaster or similar, gently rocking the lever and rotating side to side to remove the packed in particulate in the splines. Removing is a gently rock rotationally while gently pulling straight off.
Good luck! Remember to use a brass brush to thoroughly clean those splines.