Scott, the tiller head fitting can be difficult to remove. Forcing the tangs apart and using a hammer from below worked for me. The gudgeon is strong enough to take the abuse. [When all else fails, get a bigger hammer ]
With the tiller head fitting removed, removing the gudgeon and then lifting the shaft out of the shoe is how you remove the rudder assembly from the boat. The R&R description in the manual it not very detailed because the process is simple and straight forward.
There is a bit of "slack" in the shaft that results from the less than precision fitting of the gudgeon and shaft. Usually, it's the size of the notch in the rudder board around the area where the gudgeon and shaft meet that accounts for the upward movement. Not a problem since the tiller head fitting holds things in place.
It would be my opionion that your sailing difficulties had to do with sail trim and rig tune.