BTW, love your 703 Vessel View! I have the exact same 2004 320 DA and engines. Your problem is very common. Keep a spare IAC valve in your boat. I always keep two.
More importantly, the cause is carbon buildup and can be reduced significantly by using SeaFoam spray to clean your throttle body. It is completely safe and very good for your throttle body and all airflow manifolds around the throttle body. The throttle body has a ridiculously small foam filter just before the IAC. You must check this tiny foam filter too. If it is dirty, it does not matter how many IAC modules you change, the engine will continue to fail. If you do not have a replacement foam filter, then use a pair of right angle needle nose pliers and gently pull the tiny foam filter out and place it in a small cup of SeaFoam and let it soak for an hour or so. Then stuff the filter back into the small chamber. The tiny foam filters can also be ordered from Sea Ray and other Merc dealers.
About every three months during the season I pour a gallon of SeaFoam into each gas tank. Perfectly harmless and will clean the gunk and carbon out of your fuel line orifices. Your engines will run and idle much better. Just before you change your oil, pour about 6oz into your oil intake cap. Take the boat out and run the engines for about 20 minutes up to 4000RPM. The SeaFoam will be distributed throughout the oil flow chambers, cylinders, etc. and will clean out the carbon buildup. Some smoke will come out of the exhaust, but not a problem, its doing it's job to burn up the carbon deposits. You are now ready to change your oil. Your engine will purr. I also put in about 6 oz at each oil change. It will not affect the viscosity, oil additives or detergents. If you have worked on small block Chevy engines over the past 50 years, then you know how good SeaFoam is for these engines. SeaFoam works for ANY engine, gas or diesel for that matter. There are other brands but the old time mechanics I've known for years stick with SeaFoam. You can buy it at just about any automotive retailer, Wal-Mart, or Amazon. I find NAPA has the best prices.
Your mechanic shouldn't be on your speed dial list!