Oh man, I should have thought of this first.
I got to thinking about this problem and something was gnawing at me about it and I went back and re-read your original post carefully.
Do me a favor and check the fan hub. With the engine off (of course, but I had to say it), grab the fan and see if the fan blades will rock from side to side. You may notice the hub is loose. If it seems ok, then spin the fan fairly vigorously and then when you stop spinning it, it should stop failry quickly. If the hub is loose or the fan continues to spin, it is likely that the fanhub is not working properly.
The problem with the Dodges is that the fan hubs tend to wear out prematurely and when they do, they will sometimes work fair when going down the road, more because of air movement from the vehicle than the fan working. And at an idle, the fan may or may not work.
The last check is to find the spring on the inside of the hub, with a pair of pliers, unhook it and run the vehicle as before and see if the symptoms go away. If they do, the thermal spring is bad and will require replacment of the hub.
Let us know what you find.