I couldn't tell from the diagram but I'm guessing that you can use the cutter head to drive one bearing out, possibly both once you get one out and put it back in and drive it the other way. Or use a long rod. You have to be careful not to mushroom the end of the shaft. If one end has a bolt in it I would tap on it.
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.