A light Twin Engine GA pilot reported they shut down an engine due to excessive vibration and diverted to a non towered airport excessive vibration.

Narrative

I am filing this report to assist the aviation community in detailing a successful engine out procedure. I departed ZZZ3 for a day VFR flight with flight following to ZZZ2. There were no passengers and tanks were full. Flying conditions were excellent VFR. The route was frequently traveled. The aircraft was just received from routine oil change and screen inspection. Mechanic confirmed no metal in the screens and ops checks were all good. A normal preflight was made and fuel and oil levels were full. The chosen en route cruise altitude was 6500 ft. Within a short period of time after achieving cruise altitude; power and props were adjusted and the engines were leaned. Normal flow checks were made. Temperatures; pressure; prop synchronization was all good. The Autopilot was engaged. Shortly thereafter; I noticed an odd vibration for a short duration; maybe 5 seconds.There were sparse clouds in the vicinity at same approximate altitude; and I questioned myself if the vibration was a result of turbulence in the area. Another flow check was completed and everything was in the green. After scanning instruments; I looked outside aircraft and felt a more intense vibration followed by a loss of power; and then a larger vibration. I turned off Autopilot; and checked engine analyzer. Essentially at the same time was correcting for a shift in yaw. It was easy to identify which engine was suffering. I employed piloting skills to aviate; navigate and communicate; as well as identify; verify fix and feather. I shut down the engine even though the engine was producing some power and the propeller was spinning. After feathering the prop; I then closed the fuel valve supplying that engine. I am familiar with the route I was flying and the airports in the area. ATC recommended the nearby airports. ZZZ1 and ZZZ. I knew both airports and discounted ZZZ1 immediately due to terrain issues. ZZZ was in flight path to my destination.I had good altitude; good weather. I had options. I indicated to ATC I would like to proceed to my destination and I continued flying in that direction. As the flight unfolded; I was making calculations. Accessing time en route; fuel transfer and engine health. I was monitoring the good engine; verifying time en route and fuel. I made a commitment to the cross feed plan I had come up with and informed ATC I was proceeding. I knew the route would bring me close to the ZZZ airport. In the vicinity of ZZZ; I was not happy with the temperature trends on my good engine. I informed ATC at that time; I was going to divert and go into the ZZZ. When I informed ATC that I would divert to ZZZ; ATC elected to [grant priority handling] for me. While everything was looking good; communicating; navigating and aviating; I did not feel the need to [request priority handling]. I asked for winds. I prepared and set myself up for a single engine landing at ZZZ. The landing was a non-incident. There was no further damage done to property or to the aircraft. There was no traffic at the airport; and there was no staff available. It was a non-towered airport.