Jim, I experienced the same behavior on my E27. There are three potential sources of tiller play that I identified:
The brass "H" tiller fitting was not tight at the top of the tiller post. I had a machine shop run a bead around the inside of the fitting, then filed smooth. That was a good thing.
The cap at the top of the rudder post should be held tight by a bolt. I replaced the existing corroded bolt, then cranked it down with a lock washer. That was also a good thing. If you do this note that the through bolt on the cap should remain in place.
These two actions took care of most of the action. The only other source of wiggle (assuming your rudder is secured to the stock) is up and down play through the cockpit sole. I'm sure that a shim could be installed, if needed, but I wanted to maintain adequate clearance between rudder and hull.
While doing these things I took the down-time opportunity to refinish the tiller with Epiphanes gloss vanish - that was a really good thing. Good luck.
Hans
Hedgehog E27 '76
