9.9 4-stroke falters after an hour

[beckoning]

Someone out there must know how to solve this problem. My 9.9 (presumably 2009) Mercury 4-stroke kicker motor runs good for an hour at 1200-1400rpm, then it begins to cough and sputter and run on one cylinder. I put it in neutral, rev up the engine (3000rpm) to clear it out, put it back in gear (thus, put a load on the engine), and it returns to running on 1 cylinder. It has been doing this for 4-5 years. Two years ago, I changed the prop to a shallower pitch so the motor would run at higher rpm to maintain 2.5mph, and that seemed to solve it for awhile, then it started again. Back at the hoist, I have removed the plugs, cleaned or replaced them, allowed the motor to completely cool down, and it ran fine for an hour, then loaded up again. There are no carburetor adjustments...it is all preset at the factory. Most times, when it runs on one cylinder, and I reduce the speed to put it in neutral, the motor dies. I crank up the throttle in neutral to restart it, and black soot covers the water behind the boat (don't tell the EPA). I use only ethanol-free gas, keep the tank full, replaced the fuel filter, and make sure the choke is not engaged. When it has run well, I use it to drive the boat (19', 3000lbs) at nearly full throttle to burn out all the old fuel, and it still repeats the process the next time out.

I really need some help with this and hope someone has dealt with this problem and give me some good advice.