I had my Merc 115 EFI (2006 Yamaha block) serviced in late October. Complete change, fluids, plugs, seals, etc. Sat all winter waiting for annual trip to Yellowstone Lake. Didn't start the engine until early August at the Lake. It started fine but ran rough.
Did everything you did, but one thing. I hauled the Far West to the dealer (400 miles round trip) but he was reluctant to do a make an appt. until a few months went by. After some earnest exchanges, including several insults - me included, he had his mechanics to a quick analysis. Guess what? The number 3 spark plug was defective. It was brand new but defective. New plug and I returned to the Lake for the rest of the boating season. No problem after that. Engine ran fine.
Lesson for me? The Merc EFI will start on three cylinders, but just limp along and not go on plane. I have the complete service manual for the 115 Merc EFI, but it was sitting at home 200 miles away. Really careless of me, because with it I would have been able to make a quick diagnosis. I had four (4) used plugs aboard which were OK. We live and learn.
John