Is it still P0344 (Camshaft Position Sensor Circuit Intermittent) only, or are you popping other codes? I realize your issue seems to be load/heat related, but hear me out.
If your OPDA shaft wobbles (even if only under certain conditions and only for an instant or two), this will cause this code to pop since the camshaft sensor and OPDA shaft tone wheel air gap is not consistent during the wobble. It goes out of spec and the signal is lost as seen from the PCM. I've heard of folks having to replace their new Crown unit just after installing with another new Crown unit after experiencing the wobble. Crown isn't perfect either...
You can pull the OPDA cap (2 screws) and watch it spin with the engine running. See if you can detect any wobble at idle as the tone wheel spins.
Here is my story that is somewhat related, same code, different conditions:
- About 6 months after the Crown OPDA replacement, I added a thin shim (foil washer I made) to pull the camshaft sensor back away from the OPDA tone wheel a tad bit (~0.001-.003").
- In very cold weather (~0 degrees F), I was getting a P0344 (Camshaft Position Sensor Circuit Intermittent) on start. I could dupe every time on a 0 degree day. After warm, no issues. This is because the tolerances are so tight and the OPDA shaft (with tone wheel) likely wobbles ever so slightly on startup in this drastic condition.
- No issues or codes since, but still keeping an eye on it.
Next, even if the OPDA is in good order (no shaft play), on higher mileage engines and sometimes without higher mileage, tolerances are off just a bit on a spinning camshaft and tiny adjustments like this become required (unless you want to rebuild the engine). I've seen a few manufacturers selling these shims for similar camshaft and/or crankshaft sensors due to the "old age" out of tolerance conditions. This is our only option since we can't adjust the cam sensor "air gap" on the 4.0L.
Here is an example of a crank sensor shim for a Chevy Vortec. Check out info about why they are prescribed:
https://www.eficonnection.com/home/product/sensor-shim-kit
Finally, the aftermarket camshaft sensors and even the newer Mopar sensors, have been reported to have problems operating in the cold without throwing a code. Not sure if they wold have the same issues under high heat conditions or not, but thought I would also throw that out there.