Well, after a long search, it looks like I found my boat, and it's none of the above. It's a Cal 29. A little bigger than the others, but should still be manageable. By all accounts she should be stiff and well balanced, and a little faster.
The only iffy part was quite a lot of play in the rudder. It could be just the bolts holding the tiller, but then again could be something else. Could this be a serious issue?
We owned a 1976 Cal 2-29 from inception through 2011, sailing her everywhere from San Francisco to Mexico and later on both the east and west coasts of Florida.
During the course of our ownership our rudder shaft eventually wore the rudder tube and became "Loose". (Some here have claimed that the shaft had bushings/bearings but that was not the case with our rudder--perhaps others.) The fix was pretty straight forward. We dropped the rudder, thoroughly waxed it and then covered it with bond breaker and then remounted it, blocking the blade in the proper position. While the blade was dismounted, we drilled roughly 3/16" diameter holes at roughly 90º intervals around the top of the tube, roughly 3" below the cockpit deck with a second row, offset from the first roughly 1" lower. With the rudder reinstalled in the tube, we created a "tinker's dam" around the shaft at the bottom of the tube with plasticine modeling clay. With that, one can inject thin epoxy into the tube until it begins to drip from the second, lower, "weep holes". With that, a little blob of modeling clay is pressed over each weep hole in turn until the epoxy cures. The epoxy will fill the interstitial space between the rudder shaft and the tube and, once cured, creates a firm mounting shaft for the rudder. A few twists of the rudder will free it and you're good to go. (We did ours in one go although you can also inject the epoxy in lifts, if necessary.)
We made the foregoing repair to our rudder in, roughly, 1989 and the rudder was still firm and functional when we sold the yacht in 2011. (Interestingly, the yacht has since been returned to San Francisco, now sailing out of Alameda.)