John45 - I had the exact same issue and you hit it dead on. Stumped 3 auto parts store guys, the Dodge dealer, and a salvage yard.
Used the rear door activation kit (came with the car when they decommissioned it), and put it back together - door stuck shut. So I tried the other side, but this time, experimented with the latch before putting it back together. Same thing. Would get stuck "shut".
Finally found out it's what you're saying - the exterior door handle cable is the culprit. If the latch is stuck in the closed position, you can unseat the light blue part of the cable housing from the white bracket, which then lets the lever fully retract back and "reset" the latch. Then pull on the cable... latch opens.
You just have to be really careful that this cable isn't too tight. In my case, the housing broke from the blue plastic part, and that one millimeter or so is enough to not let it retract back enough and "reset" the latch.
Laumannlaw:
Kit is from nenno-products (.com), or just buy a door at a salvage yard for the same price and rip out the guts.
Center console:
Any regular console from the similar model range of years will fit, but the floor shift will be missing.