Well, I took the advice given here and today I jacked the Acclaim up to check the CV's again. Like before, I couldn't really see or feel anything that would say they were the source of the problem. The only thing that looked a little suspect was that the boot on the inside passenger CV seemed to be puffed up a little. When you squeezed it, it felt like there was pressure inside. This made me think that maybe water had gotten into the joint (as suggested here). I had been driving the car and it was hot. Any water in the joint could have pressurized the boot.
Based on this and the advice I got here (on the board) I pulled the passenger half-shaft for a closer look. Opening the boot showed that all the grease was still there but that I might have a little moisture in it. It's color was a little brown. I still could not see or feel anything wrong with the joint, but since it was out, I went and got a replacement.
Short story is; problem fixed. The car no longer shimmies at the 38 - 45 mph range like it did. All I can figure is that (as suggested) the bearing rollers in the tripod joint had worn the slide surfaces so that they were no longer flat but indented in the same shape as the bearings (concave?). Therefore, under acceleration, either the bearings become locked in these grooves or they try and climb out of these grooves which puts lateral force on the shaft and pushes the engine to the side (because the tripod can no longer slide and do it's job).
The moral to the story is, you really can't see or feel this wear in the joints. I guess experience (probably gained by trial and error) is what will tell you where the problem lies.
I really appreciate everyone's help. I probably would have replace everything on the car looking for the problem before I got to the CV's.
Thanks again. You have save me a lot of time and headaches.
David Dowell.