I did the core when I had my 02. I too, received the wrong core the first time, and the second time the core looked wrong, but the inlet/ outlet pipes can be turned. When I got it the pipes lay flat, parallel to the core but they can be turned into position.

 

Job done.
what a pain in the *****.
why couldn't mopar cut a slot in the firewall with a gasketed cover plate, to pull the core out of the box. stupid.

 

did that fix your heating issue?

 

Yes, it took care of the problem. I also installed a wye strainer in the heater supply hose. Put about 50 miles on it, and inspected it. Caught a few pieces of crap.
I also cut open the supply side of the core, using a cut off wheel. Ignore the silver shrapnel, that's from the cut. Note how small the passes are, and, note the debris found.

 

And now............... the damn radiator blew. must be a small crack, was able to limp her the 2 miles home.

 

radiator in.
filled and bled.
boy1 to take her for a local spin to see it there are any more surprises.