Hi, my name is Ed. Welcome to Just Answer!.
I have a feeling that you may have jumped time on one of the cylinder head banks, Scott. Each engine bank has its own camshaft and timing chain (overhead cam type), which means you can have one side timed correctly and the other side can be skipped a tooth or two.
I'm pretty sure that your 03 Ram truck will have a single upstream oxygen sensor
that will be mounted at the convergence of the two exhaust downtubes before
it goes into the catalytic converter unless it's a special emission market application like CA or MA/ NY. With a single 02 sensor sampling both engine banks' exhaust at the same time... and very dissimilar air-fuel mixtures between banks being mixed together... you can wind up with the bad side looking black and the good side being run too lean.
If you happen to have two
upstream sensors, you may simply have a bad 02 sensor on the driver's side, which is the sooty black side. When checking for 02 sensors, it's important to understand the difference between the upstream and downstream designations. An upstream sensor is always installed ahead (upstream) of the cat, which downstream sensors are after. Only the upstream sensor will have an important impact on air-fuel mixture, so let's just concentrate on that for now.
Oxygen sensors look like spark plugs with a 4-wire connector attached to the top end by the way.
If you find that you have only ONE upstream sensor (also called the 1/1 sensor), see if you can do a compression test on the engine to compare the two banks. A cylinder bank with "slow" cam timing will also have reduced compression as compared to the good side, so what's important is that you have numbers that are within 10 psi or so of each other. Lowered combustion temperatures and reduced breathing on a bank with slow cam timing can also contribute to the sort of sooting issues you've seen on your spark plugs.
Normal squeeze readings run around 170 on this engine when checked at wide open throttle and ten compression strokes (all plugs removed), but compression gauges vary... so rely mostly on consistency between the two sides. Consistently lower numbers on the sooty driver's side as compared to the blistered side will almost certainly mean you have timing chain problems.
Let me know if you have any problems or questions, Scott. Good luck!