Sea Ray

I have exactly the same boat with same engines / B3 drive also but a 2003. At the beginning of the season, I replaced the IAC, the IAC muffler, the spark plugs (in case of a bad one), still difficult to start and to keep a stable idle. There is a fuel filter on the fuel line close to the tank connection. Did you ever change it. I changed the filter and everything was better. I did not take a chance, I replaced it also the one on the other tank/engine. They both started right away and run fine after.
Lately, I had one engine that have unstable idle and when I was trying to increase the throttle, the RPM was going down, no power and something even the engine was stopping. Sometime, the engine did not even start, was waiting minutes and try again and start. We put the computer on it and found a problem on the 5 volts bus on the PCM 555. When the idle was normal, the voltage was 5V sharp. When the engine start to have unstable idle, we noticed that the voltage was dropping below 3 volts on the 5 volts bus and we had error code 133, In the manual, 133 means 5 VDC PWR LO. For me, it was clear that I had a problem with one of the 5V sensors. See attached file.
I discussed with my experienced mechanic and he told me that it is commun to have problem with the crankshaft position sensor (e on the drawing) on 496. He gave me one that he had in is tool box to try. I installed it but no change on the engine i.e. bad idle again. I put back my sensor. On the drawing, you can see (d) TABS sensor (Transom circuit). On Bravo 3, there is a trim position sender (3 wires) in the water that is taking is 5V supply from the 5 V bus on the engine computer. I disconnected that d harness and my engine is running like a brand new for weeks. I will have the trim sender (Mercury # 8M0095310) replace this coming Fall when the boat will be out of the water for the winter (we are on Lake Champlain, NY). Now, the drive up/down switch work only to lower the drive. The raise/limit circuit is disconnected and to raise the drive, the trailer switch still work but both drive go up at the same time.
In conclusion, a problem on a drive position sensor in the water can give you hard time with your engine. As an Electrical Engineer, this is a very bad design that Mercury done. I heard after my adventure from a friend that he blown a computer some years ago du to a bad trim sender also. I have been lucky, mine is still ok, a PCM 555 unit is very expansive. If you can find Mercury Service Manual # 33, it provide a lot of information on your engine computer. The drawing is coming from that manual. When you will have found the problem, let us know. We learn from the others. Good luck.

When I had that issue replacing the IAC valve seem to fix it. These valves are only good for about two years.

I have exact same year, make, and model boat and engines. You described exactly the same issue I had three months ago. We changed the fuel filter and IAC. You will also need a tune up with spark plug cleaning or replacement.