No promise of a magic bullet, but some things to consider:
You said you replaced the PCM. Which came first: Bad PCM or bad coil? I ask because there have been several instances on this site over the years of the PCM failing such that the outputs that drive the ignition coils stick on with either a high duty cycle ('on' time vs. 'off' time) or solid 'on'. There is high current flow and heat generated during coil 'on' time. The coils are designed only for normal ignition signals, which are very low duty cycle. Likely your PCM output for that coil failed giving a high duty cycle or solid 'on' for that coil, which is why it melted and failed. Usually that PCM failure affects more than one coil output. I wonder if you have one or more walking-wounded coils that need to be replaced
- bad enough to cause rough running under certain conditions, but not bad enough to throw a code.
As far as a connection between the rough running and speedometer jitters, I can only wildly speculate. For example, if you have a "wounded" coil, it may be partially shorted - i.e., still marginally operating but pulling lots of current from the PCM under certain engine speeds/operating conditions. That could be affecting operation of other circuits, like the tranny speed sensor circuits (which are also in the PCM) at the same time as the rough running.
Other things that come to mind:
• Spark plugs: Your single plat plugs are fine. Double plat is only needed for ignitions that operate plugs with reverse polarity - not the case with these cars. The NGK/NTK ZFR5LP-13G (AKA 7781) that Ron mentioned is the plug number stated in the '02 FSM. The prior year FSMs called out Champion RC12PEC5 (AKA 3034). RC12PEPB5 (AKA 7034) is the double-plat version of the same plug. My guess is that a previous owner or mechanic replaced the factory NGKs with those. Either should do fine. Is it possible that Chrysler switched to the NGKs due to issues with the Champions? Might not be a bad idea to replace them with the NGKs, but I would be surprised if that is causing a problem.
• Spark plugs need to be torqued to the proper value (20 ft-lbs) to ensure that they make good electrical ground contact with the head - poor electrical contact can lead to rough running.
• There is a spiral-wound spring-like electrode coming off of the output of the coil that makes the electrical connection to the top of the spark plug. More than a few people have had corrosion develop between that electrode and the output of the coil causing poor electrical conductivity and poor running. You can pull the electrode out of the coil and clean the recess in the coil and the electrode of corrosion - put a light coating of silicone grease (AKA dielectric grease) on the coil output and the electrode before re-assembling. New coils come with the electrode, so that would eliminate that issue on coils that are replaced.
• Make sure the two screws that attach each coil are tight (60 in-lbs). Probably not a big deal, but may be important for cooling of the coils (by heat sinking to the valve covers or heads).
• There is a black part (box shaped, 1/2 to 1" on each side) that is attached by a small stud to each valve cover or head - there will be a single black wire from the engine harness to the black part. It is a capacitor that filters ignition noise from the electrical power. For the capacitor to do its job, the wire has to be intact and connected, and the capacitor has to be firmly attached to its bracket (which is screwed to the valve cover or head).
• Poor power (+12 volt) and ground connections between the battery, engine, and computers can cause all sorts of quirky little problems like this.
I don't want to get your hopes up, and I realize that you will have to spend money with your fingers crossed to check some of those things. Sorry, again, that I don't have suggestions for diagnosing without buying new parts.
As always, comments from others are welcomed.