Try the shaft first and see how it goes. That should solve the problem. If you continue to have slippage though, then
replace the spine.
Stringy is the only member who has made the Twist N Stow conversion that I know of. He's a genius with metal and has some other great projects as well. IMO, the Classic runs well on its original rudder. Even though it's a minor annoyance to have the rudder sticking out when loading, it's probably not worth the time or expense to upgrade unless you just want a challenging project.
If the rudder is causing difficulties loading, you can 1) put the stern on a crate to keep the rudder off the ground or 2) load the boat backwards, or rudder first.
For maximum rudder control, make sure your rudder deflects equally in both directions and your turn lines have no slack in them when the rudder is centered. If you want to enlarge the rudder, Kepnutz did an excellent post on that subject.
BTW, I had a Classic for years -- what a great boat! With Turbofins it was a regular hotrod!