I've found that if you take a 1/8" inch welding rod and beat all the flux off and clean it up good, bend it 90 degrees about the last 1/2" and bend about a 3 inch 90 degree handle on the other end, you can get the short bent end under the gear and put a lot of pull on that intermediate shaft to get it out. You may have to use a big screwdriver to twist it back and forth while pulling. It could save pulling the intake.
