Unfortunately you could have a number of things not working within proper range to have a normal idle speed of 600 RPM and to start off with, you'll want to know if you have an EFI sensor out of range which may (or may not) produce a fault code. Being that you have a MEFI 3 designed ECM, there is a way to build your own trouble code reader to see if you have any codes which doesn't necessarily mean it will sound a warning horn on all ECM models of that ere. The following link offers the best advice of how to create this trouble code reading tool and offers some schematics of what the numbers may mean should you have any...
http://www.offshoreonly.com/forums/...-code-tool-less-than-$1-00-a.html#post1328705
This can be challenging without the aid of a Marine Scan Tool telling you what the sensor parameters are but using a multimeter could help verify their parameter values too along with an OEM service manual to help guide you in the troubleshooting sections of the manual.
A few examples that could affect staling could be if the throttle position sensor has become out of range in the low settings, it could affect idle RPM and kill the engine.
A defective MAP sensor, engine coolant temp sensor, intake manifold sensor as well.
Low fuel pressure to the TBI unit and Low to too High fuel flow values out of the TB injectors could cause low RPM stalls.
Faulty ignition sources like the coil, coil wire leaking, leaking "spark" plug wires, fouled spark plugs, ignition module/or sensor under the dizzy cap depending on engine model....Yours don't have the module design that thoroughly controls timing. Timing is more controlled via the MEFI 3 ECM.
Dirty throttle body and TB plates, misadjusted throttle cable, engine vacuum leaks, bad/old fuel.
Do you have a Bravo stern drive or Alpha drive? If alpha, again, misadjusted shift cable/throttle cable movement that's out of sequence cold be affecting the shift cut out switch located on the shift cable plate mounted on the engine and vibration from a rough idle could possible be pushing on the cut out switch. < Remember, these are just ideas being thrown out there for one to look over.
Sorry to read you bought a new oil pressure switch because unfortunately on this EFI engine model, the oil pressure switch doesn't directly affect fuel pump control, it's done via the ECM that turns on and off a fuel pump relay. Mercruiser "carbureted" engines only use the oil psi switch to control electric fuel pump power.
Even though the fuel injectors seem to stop flowing fuel and the engine dies at low RPM, you'll have to try and determine if the Relay/ECM system is turning off the engine at idle which I'd say no it's not happening because you can keep it running by manually advancing the throttle.
So by advancing the throttle, essentially you are giving the engine more air, more fuel and more timing and many parameters are constantly changing as well with each RPM advanced.... So now you'll need to try and determine if the engine seems to be overly rich in fuel or under fueled (running to lean). To inspect for this condition is by first looking at the water flow coming out of the exhaust system to see if you see a heavy fuel/water mixture plus maybe a rich smoke smell in the air and also pull out a few spark plugs to see what they may look like too.
Engine timing would be hard to check at idle if it keeps dying, but with the info within the link above you could try going into service mode to see if the engine will run on it's own as being a MEFI 3 ECM, it should rev the engine up somewhere between 1200 1800 RPM automatically once put into service mode. And if need be, you could go up your known working 1000 RPM, go into service mode then bring the idle down and see what happens. It may run, it may die.
At some point you may just need to check for an engine vacuum leak both by spraying something like carb cleaner around the top of the engine and also connect a vacuum gauge up to see what the internal engine vacuum system is doing/reading.
First pull out some spark plugs to see what they look like. Then remove the throttle cable from the TBI throttle stud, clean the throttle body plates and walls where plate almost rests. Once clean and the throttle cable still removed, put the spark plugs back in and see if it will start normal...If not open the throttle, get the engine up to temp of 160 degrees, slowly bring the idle down and see if it will idle at 600 RPM.
Maybe posting a video of how it runs and dies might help too.
Hope this starts to help in someway, good luck.
