Even though the u-joints might feel tight take into consideration the car weighs in at about 3200 lbs, that is a lot of weight and force on the u-joints. You are not going to be able to get any movement out of them unless you take the complete weight off the tires and then slip the car into neutral. Then get underneath to where you can see and gently rock the tire back and forth on both sides. You might also put a bottle jack under the wheel assembly and lift it up gently to remove all weight and compression from it.
I will continue to say I think it is the u-joints.I had the same problem and went through the same process you are going through and had the same comments told to me before I found the problem. And it was Vigman who finally came to the rescue and pointed me in the right direction.
Think about it, a loose tie rod end will cause the wheel to move and wiggle...not the whole car from side to side when the gas is applied and let off of. As the half shafts act as the lower a-frame in the rear suspension, logic would dictate they are close to the problem. When you give it the gas you are binding them in one direction, when you let off they momentarily "float" causing the wiggle, then as the car slows down and engine brake takes over they bind in the opposite direction.
And I would be extremely careful driving the car, because if one of the half shafts comes loose, it will cost you more then 15.00 for each u-joint to replace all the damage. Also if it were me and it had that many miles I would change them anyway if nothing else for peace of mind.