I have a chevy that is almost identical.
Due to less than spectacular results seem with Mobil 1 in my engine (4.3L V6), I think that a dino (or maybe another syn oil) is the best bet.
I currently use castrol 'Start Up' 5w30, and like the behavior at startup after sitting for a week in the cold. Dont havea ny used oil analysis on it though. I would consider a syn oil with a relatively high 30 weight viscosity and a good ester content (which I believe provides the start-up protection by remaining on the metal surfaces).
The only oils Ive been considering trying for my situation are German castrol 0w-30, Mobil 1 0w-40, and mobil 1 truck and SUV 5w-40. the first two are heavy 30 weight oils/light 40 weight oils, which ought to be good for protection in my engine, and 0w- which should allow good flow at startup. The Mobil 1 5w-40 I believe has a pretty high ester content, and I think the 40 weight should give pretty good protection, though I wish it was a lighter 40 weight, just about a 30. These oils I believe would give the best startup protection and deal with the sitting, potential for condensation, and requirement of a clean engine. But I cant say without driving for many years due to the miles per year that I get that one will be better than pennzoil 5w30 or Castrol Startup.
If it does not use any oil, and comes out pretty clean, I think how youre doing it is a good way to go. Unless of course you can find a good synthetic oil that produces consistently good results in the dodge engine.
Weve seen lots of good used oil analysis on modern conventional oils. Just use a good one (pennzoil, motorcraft API SM premium blend, GTX, Startup), and I think itll be OK. As an example, the best used oil analysis Ive seen for my truck engine have been with pennzoil. I doubt that a Chrysler truck engine will yield that different of results.
Hope this helps,
JMH