on my 2010 3.5 i've found if it gets into overdrive at about 40-45 mph and you hit a small hill that doesn't cause a downshift the car will lug up the hill. you'll hear/feel a small vibration and as you stated it goes away as soon as the car down shifts by tapping brake, letting off the gas or giving it more gas to cause the downshift. i also noticed when i lived in Michigan it was always at a particular point of my drive to work. stop light before a slight hill that would always hit O/D about the time i hit the bottom of that hill. it drove me nuts!
what i figured out over time is that the car is programmed from the factory to get the best mpg's it can. so it tries to keep the car in the highest gear it can at all costs, which means it shifts into overdrive about 5 mph too soon causing that scenario. does this sound like what you were experiencing?
as for the code, someone who is much more experienced in troubleshooting will be of more service than I am.
what i figured out over time is that the car is programmed from the factory to get the best mpg's it can. so it tries to keep the car in the highest gear it can at all costs, which means it shifts into overdrive about 5 mph too soon causing that scenario. does this sound like what you were experiencing?
as for the code, someone who is much more experienced in troubleshooting will be of more service than I am.