Which cylinder head do you pull to remove the airbox?
You use a little heat (leave it out in the Arizona sun right now) from a hair dryer to soften the parts or area that hangs up, and pull it out the back.
If you want to take it out the front you need to remove a cylinder head, cylinder and studs. ;-)
As for the carb, if the starter motor is the correct/original size the problem is due to the carb rubbers either being old and perishing or having been tightened up wrongly.
Loosen the front clamp on the rubber, lift up the carb, and retighten the clamp, then do the same with the rear clamp. It doesn't give a lot but it should give enough unless there is something really wrong with the starter.
Remember that if you are going to remove it you should still keep the breather box and place a filter on its outlet to avoid sucking dirty air into the engine.