P0340 code still rough idling?

It sounds like the timing chain can be worn out, also I would do a compassion test to see if the engine is hurt or not, you can upload a short video of the engine cranking from under the hood and I can tell if the engine is okay or not.

P0340: Camshaft Position Sensor Circuit Malfunction

The following is from DTC P0341. The EI module uses capacitive pickup plates located under the 1/4 coil pack to determine the polarity sequence and voltage amplitude of the cylinder 1/4 secondary ignition. The PCM supplies 5 volts on the signal line and expects to see the cylinder #4 signal wire go low after every 14 crankshaft pulses (2 revolutions). This is used to determine the position of the camshaft, except under decel. The PCM only uses the transition from 5 to 0 volts as a valid TDC compression #4 cylinder signal.

This guide can help as well:

https://www.2carpros.com/articles/repairing-engine-rough-idle-issues

and

https://www.2carpros.com/articles/how-to-test-engine-compression

Please upload pictures or videos in your response of any problems so we can see what to help you with.