[tucsonjwt]

I know nothing about steering, so of course I will offer an opinion. If you replaced your steering box and everything was tight after that, then I think you might have gotten a bad steering box, or your rag joint needs replacing. Steering boxes are pretty simple, and I have had a "cheap" Autozone rebuild for 5 years with no problems, so I think a bad box is unlikely. Unfortunately, you can have problems farther up the chain in the steering column, which is much more costly to repair, and more difficult to diagnose, and something I leave to professionals. Whenever I crack open a steering column bad things happen.
Obviously, you know how to check the suspension components, and you say that all is tight there, but...
This sounds like it is worth a trip to your local front end/suspension/alignment shop for a free estimate of repairs. At least call them and describe your symptoms. If they say everything is OK under the hood, but you still have sloppy steering (especially at speed) then I suspect the steering column. I have gone through all of these parts mentioned on my squares and the most expensive and most troublesome was the steering column. Since this is not your daily driver, you can crack the column and start looking for trouble. There are places online that provide step by step instructions on disassembly and repair - but at least you will be able to identify for sure that you have a bad column, and get tips on diagnosis, even if you send the work out or buy a rebuilt. One telltale sign of a bad column is a clicking or snapping sound when turning the wheel, but you would notice that if driving with the radio off, a/c off, and windows up.
You could, of course, have both underhood steering component and steering column problems, but I would start under the hood again first - cheaper to fix, especially the rag joint.
One other possibility is a wheel bearing, but you can check for that easily with the front end jacked up, and the alignment guys can spot this for sure.