Will it run ok on a water hose and muffs? If so, then it doesn't have enough power to overcome the water pressure from the exhaust being a couple of feet under water. I've had several motors over the years that would run fine out of water on a hose but would stumble, die, sputter and otherwise have a hard time staying running until you can get it going. Start with the basics of compression, spark test etc. Spray some engine cleaner into the carbs while its in the lake at idle or slight high idle. The carb that doesn't lose as many rpm's when you spray it, is the cylinders you are after. The carb and cylinders that bog down the most are the ones hitting the hardest.
