Hi,
I don't know these engines and have never worked on one so this is just me spitballing about things that could be common to many engines.
You may want to check your fuel/water separators and filter strainers and compare them after the outboards have sat overnight.
If you find the port has some separation in the water catch or debris in the filter bowl that might explain the surging at cold start up and then no more until they've sat for a time.
Or you could just service those items to see if it makes a difference.
Other things that come to mind would be a sticking idle air control, possible intake air vacuum leak or a dirty throttle body.
Most throttle bodies can be cleaned using the appropriate throttle body cleaner
BUT...it must be done carefully.
I think a sticking IAC would probably act up all the time but you never know. Heat from the engine could free it up.
Also, most IAC valves have some sort of filter screen. The valve and screen can probably be CAREFULLY cleaned with throttle body cleaner but, again. I have no experience with these.
A vacuum leak could be temporarily "self sealing", in a sense, as the engine warms and components expand. So it's a real possibility for this type of symptom.
Vacuum leaks can be located by spraying carburetor cleaner at strategic points of the intake manifold and noting any change in engine speed.
Less likely culprits (in my opinion) might be a MAP sensor starting to fail or a possible fuel injector leaking/sticking.
You could rule out the MAP sensor by simply swapping it with the stbd.one and seeing if the problem follows or stays with the port engine.
Just some ideas.
Hope you get it sorted.
Good luck.
