Hope I don't come across wrong here but crank/cam speed sensors are notoriously hard to prove good or bad. The output amplitude of the pulses can degrade/decrease, especially at low rpm, to a point where the PCM/ECM considers the "signal" valid but may start using the other (cam vs. crank) sensor for timing, etc. It's a redundant feature that is present in the firmware of at least some ECM's/PCM's.
The problem is that this condition (from experience), which is actually a fault, may or may not set a code... worse yet, any codes set may or may not be "instantly" cleared when the condition, as seen by the computer, "goes away". In other words, a weak crank or cam speed sensor can seem intermittent when it's actually just plain "weak". You can "see" a MIL then not get any codes.
The cam sensor has all the information but half the resolution of the crank sensor. The symptoms can be as "small" as poor economy from less than ideal timing to more obvious things like loosing the tachometer or longer crank times to start (even if it runs normally once it starts). Since several of your symptoms also appear to be ASD related (things that don't operate until the engine is "turning") they only increase my suspicions.
FWIW, any time I see these "type" of symptoms, I just want to SCREAM out "replace that stinkin sensor". Don't probe, measure, or even think about anything else until you're 99. 999% sure the sensor isn't the culprit... and because of its nature, replacement is about the only way to be "that" sure.
I'll be honest... I switched from "reading" to "scanning" this thread as soon as I saw two things: intermittent tach "operation" and a temp. MIL with no codes... I am also concerned that those codes you posted a few days ago are simply the result of your troubleshooting efforts vs. the root problem. All three of those "can" be set by simply unplugging the pigtail with the key on. It is very nice to have a way to clear your own codes.
My 1st direct experience was on a 4. 7HO gas engine but that one will live with me forever... I now carry spare crank and cam sensors every where I go. I've already replaced them both on my '06 Cummins and keep the old ones in the truck, since they were apparently OK. No regrets, once they're ruled out you can move on. I would not replace that PCM w/o replacing both sensors first. Dealership techs, even with a scanner, can't see much more than you have already described in this thread. Many new PCM's have failed to fix many old problems... Worse yet the problem can go away then come back later since the weak signal can get just a little bit stronger with a brand new connector. The amplitude of those pulses are probably in the low millivolt range or less... regardless of the rms or dc levels you are seeing with a meter on the harness.
Enough said by me... for now anyway. This is one of my all time "over thought about", "over preached about" issues. Sorry to go so long. Good luck.