I don't think the 4 cylinder tj came stock with a Dana 44 rear end. I believe they only placed the Dana 44 on the rubicon model and some 6 cylinder jeeps with the tow package but I may be wrong. The 8.8 isn't a bad choice the difference in the length of the Dana 35 and 8.8 is not much of a...
I would trace the power wire back to the pump and see where the power is lose could be a torn wire or maybe a ground wire issue, could it be that the pump just quit working on you?
This is what my 4cyl tj shroud looks like the fan is near the edge of the shroud
If you have an overheating problem I would look into a fan shroud. You want the cooler air coming from the radiator vs. The outside air.
I had this happen to me a month ago so i installed a stop valve from a sprinkled kit the ones were you turn the valve open and close. It seems to do the trick since most people dont know how to get behind the fender on my tj