Some of these east-west mounted V6s can be very difficult to access the rear bank of cylinders. A quality workshop manual will detail how to remove the rear rocker cover and spark plugs, and there are also some very good online tutorials you can tap into.

The fact that no error codes have been logged suggests that the spark plugs are at fault. In some cases, on-board computers can detect a bad ignition lead or coil, but will not recognise a dud spark plug. But oil leaks can also cause misfires if the oil gets into contact with the leads or spark plug contacts, too, so the leaks need to be fixed as well. The spark plug theory is also supported by the fact that the miss is occurring under load, which is when an ignition system is working its hardest.

The cold cranking power required to start an engine first thing in the morning when it’s cold is much higher than when it is a little warmer, as it is later in the day. Make sure your battery has sufficient cold cranking power to do the job. If the battery is too small, even if it’s new, it might not have the power needed to crank a V6. If it does have sufficient power then look to the starter. If the starter is not throwing in it could be worn.

There shouldn't be any issue with leaving the maintenance charger connected to the battery, and other than the inconvenience if having to reset the clocks and radios there shouldn't be any issue caused by disconnecting the battery. After all you have to disconnect the battery when changing to a new one.