I jacked up the car and found two things wrong with the steering rack.
The first and most obvious was that the outer tie rod end on the left side was adjusted all the way in to the point that there was no room for further adjustment and there was plenty of adjustment available on the other side.
The second thing is that the rod on that side also seemed excessively loose at the inboard end compared to the other side. With the steering wheel centered, I could easily move the outer tie rod up and down and, to a lesser extent, back and forth.
After watching the video that Nick linked to, I checked the jam nut on the inboard end and found it to be loose. I tightened up the bushing and the nut per the instructions which stiffened it up a bit. The jam nut on the outer tie rod end on the right side was also loose so the next thing I did was to center both tie rod ends and did a quick realignment making sure there was no slack on either side.
The play in the steering is gone completely. I still need to get someone else to do a proper alignment now, but at least I don't need to buy a new rack.
The bad news is my radiator (Griffin aluminum cross flow) developed a bad leak on the test drive; halfway up the outlet tank where it appears to have been making contact with the aluminum shrouding and wore through. It never came close to overheating, but half my coolant drained out and I had to stop at a little bar & grill to relax for a couple of hours while it cooled enough to add some water and head home.
Overall, a good day. The car ran and handled like a dream. The parlimentary representative for my constituency lives across the street from where I was stopped and he came over to check out the car. So I made some new friends discussing cars and politics while I waited.
The Cobra got me home easily with the leaking radiator and now I can look forward to pulling the rad and taking it in for patching.
Thanks again Nick and Bob for your help - another big part of the joy of Cobra ownership.