At idle the butterfly's are (normally) totally closed, so sync at that point is not overly important.
What would have more of an effect would be a slightly lean condition (idle mixture screw not backed out far enough) or an overly rich condition (backed out too far) which could cause rough idle due to a very minor flood.
Unless you have really messed with the trigger linkage it won't just go out of timing on it's own - so if you simply unhooked the linkage and then put it back when the carbs were reisntalled the timing would be close enough that you wouldn't notice a difference.
The muffled sound (could) be caused by restricted exhaust. It sounds fine on land but once you add water into the mix the exhaust pressure just isn't what it should be and that can cause crappy idle, stalls etc at lower rpms.
It's not overly common but on models such as this that have an exhaust tube (instead just a big exhaust horn like many models), particularly ones run in salt water, can get quite restricted (like build-up in a waterpipe from minerals in the water).
I have seen exhuast tubes so closed down that you could barely get a pencil through the hole that's left.
So first maybe try resetting the screws - all the way in until lightly seated then back out 1 1/4 turns.
And if you feel ambitious maybe pull the lower unit and take a look up the housing with a flashlight and see what kinda shape the exhuast tube is in.
The exhaust tube is about 2'ish inches in diameter and extends part way down into the housing (leg) - the walls of the tube should be "sooty" but there should be no build-up at all on the inner walls.
If there is, it can be cleaned out, but it's a little more involved process - have to pull the powerhead to get at it properly...