Having owned two Grampians, I'd say that Jims method is best. The rudder hangs down in the tube, supported only by the pin which secures the rudder into the boat. It rides on a large bronze washer which sits on the cockpit
sole or may be imbeded into it. The tiller head
is keyed and held in place with a tightening bolt. As time passes the washer gets opened up in diameter, and the pin wears a notch on either side of the shaft. It also works loose and allows water to get into the plywood core
of the cockpit sole. So putting a large plate, drilled for the shaft diameter will tighten up the top end. I would route
out the sole about half the depth
of the plate, epoxy the plywood
and rudder tube junction (checking for any deterioration of the plywood) and then install the plate.
I would also suggest that you examine the tiller head
and tiller fitting as the twisting motion of using the rudder will over time elongate the holes in the tiller head. There is only so much material here so if its been drilled out for a larger bolt once or twice you may be nearing the point at which the tiller head and fitting need to be replaced. I believe this is the cause of your problem of having to chase the rudder. Wear in the tube or erosion of the support washer would not affect steering
very much given the length of the tube and the clearances within. Block the rudder amidships from below so it won't turn, then check the slop in the tiller head.
As for the tube bottom, the clearance between the shaft and the tube is pretty tight. It may be possible to have a bushing machined from plastic which you can put on the shaft and have it slide into the rudder tube as the rudder is reinstalled from below.That will tighten up the clearance at the bottom. Alternately, remove the rudder and shaft, coat with release agent and re install after drilling a hole into the shaft about 5 inches up (crawl under the cockpit sole to do this). Seal the shaft as well as you can with plasticine from outside, and then inject the epoxy/graphite mix into the rudder tube.