Before you do anything too drastic, or start to spend money, I'd suggest just giving it a little thought. Maybe open the cover, put it in neutral, spin the output shaft by hand, and see what is going on, in there. The potential problem is, that the rear output could end up being below the oil level. But, if you make sure the oil is up to the output shaft, no problem. Jason, and the Tri-County bunch have helped this problem with their paddles. But,.... I have been towing a CJ with a Dana 300 for well over 10 years (stock, no paddles). I have often covered over 500 miles in a day. I have had absolutely no problems. I just put the T/C in neutral, the trans in a gear (or park, for an auto), and go. I keep the OIL LEVEL VERY FULLl. I park on a 'down-slope', and get a little more oil in the 300, than was originally intended.
In my opinion, rear hubs aren't needed, removing the D/S isn't needed, running the engine isn't needed, and following the directions in the owners manual isn't needed. The owners manual, BTW, says lock the front hubs. Following these directions is a sure way to splash T/C oil, even if it is not full. From the manufacturers standpoint, I'm sure this is the safest recommendation.
Best Wishes.
bob