The plug you're thinking of is the fuel heating element and it's on the top right of the filter assembly (looking at it from the bumper). You'll be able to tell pretty quickly if that's melted, as the deformation is pretty obvious.
Your steps sound logical, and fuel supply issues due to air leakage, clogged filters, etc. are probably in the top 2 of frequently reported problems.
My recommendations are (in order):
1) Ensure you're not actively leaking(since all else is meaningless if diesel is coming out of a hole in the filter)
2) Inspect/replace filter element
3) Investigate ways to potentially replace the filter and supply assembly (new mopar design, racor filter, stanadyne filter, in-tank pump, etc.).
4) Drive it a while and see if the problem comes back
If you're lucky, you just need a filter. If you're not, then you have a leak in the head or otherwise insufficient fuel flow. I did a bleeder valve and CAT filter conversion years ago, but honestly, my problems have been completely gone since I put in a lift pump and aftermarket filter:
http://www.polter.net/~dan/pics/liberty/cummins_pump/
Dan
Since the problem goes away with the use of the primer, I'm thinking that it's sucking air from somewhere. Hopefully from the heater connection. Thanks again.