Do you think it could need adjustments even if it didn't used to smoke and now it does?
Need further detail to try narrowing the possibilities, this is a process of elimination.
Leaky inner crankshaft seals:
So the smoke is occurring the first few minutes following cold starting, after the boat has been sitting unused for a week? Or does it smoke constantly, or does it smoke a few minutes after hot restart?
If the engine is smoking constantly, not just for a few minutes following start-up, this would indicate the oil injection is supplying too much oil. Also, your spark plugs will foul more often when there's consistently too much oil. The center ceramic insulator underneath the ground electrode will be covered in oily wet soot and black, this carbon deposition will cause the plug to misfire in a shorter time than ordinary.
The plugs should have a cardboard brown color to them, black soot is indicative of too much oil or too much fuel. It's unlikely there's too much fuel though, usually the opposite is true but it's a possibility. If too much fuel, you can usually smell the gasoline wafting behind and the engine runs pretty rough. This burns my eyes thus it's what I think of when you mention your eyes sting.
That said, if the smoke is prolific just for the first few minutes then normalizes, there's a good chance one or both of your inner crankshaft seals are leaking. If the boat sits say for a few days and oil is seeping into the crankcase slowly through leaky crankshaft seals, it's right there ready and will enter into the combustion chamber at startup. This will make for a nice cloud of mosquito-killing smoke for the first few minutes at least, until the excess oil is cleared and pumped out of the crankcase.
In this case note it could be just one or both seals, if just one then only that spark plug will tend to be sooty and the other much more brown as normal. Keep in mind it takes some time for the spark plugs to reach normal operating temperature thus running on a trailer is no way to judge very well, such issues as spark plug center electrode ceramic insulator color. Basically running on the trailer only validates whether the engine is liable start in water once launched, can't tune an engine out of water except to correct for gross mistune in preparation for a water test.
So if you ever take your boat to a shop for engine or jet pump service, the boat repair remains incomplete until after the boat is water tested.
Let's say your inner crank seals are actually leaking and the boat sits unused for a lengthy period of time. In this case the crankcase will continue filling with oil from the constant force of gravity forcing oil through the leaking crank seals, eventually filling the case with enough oil the engine cannot be started without first removing the spark plugs and cranking the engine over using the electric starter to expel the excess oil through the spark plug holes and out of the engine crankcase. You'll need a towel laid over top of the open spark plug holes to absorb this excess oil while cranking the engine.
In this case, you will lose an appreciable amount of expensive oil to waste, perhaps 1/2 quart or more is possible.
Leaking crank seals are pretty common as these rotary valve engines age, the rubber lip seals that should isolate the rotary valve drive gear lubricant (2-stroke oil) from the rotating assembly in the crankcase tend to wear and harden due to heat and constant exposure to fuel. Once they begin leaking it usually starts off as a bit of extra smoke, especially the first few minutes of startup.
So if your seals are leaking, you can install a manual valve as a temporary work-around to stop the oil from flooding into the crankcase, where it's not supposed to leak toward. Leave this valve closed when the boat isn't being used and the oil is stopped from leaking past the crankshaft seals.
If after sitting for say a month or more unused, you cannot start the engine due to the crankcase is flooded with oil, it's probably due to the inner crank seals are leaking.
Clean the leaky oil injection check valves:
Another possibility for oil seepage into the crankcase while sitting unused is through one or both of the oil injector nozzles. These nozzles have a spring-loaded check-ball valve inside which normally would self-close but over time can become dirty inside, interfering with the check-valve operation. If for instance the check valve ball is not closing due to some contamination, oil will tend to dribble through it unabated, while the engine is not running. It might also be possible to cause constant high levels of oil smoke as well, I'm not sure.
Check the oil injection pump calibration:
The oil injection system is variable volume delivery. Thus as throttle is applied normally the cable attached to the oil injection pump operates a pintle valve that regulates the volume of lubricant being injected into the intake tract along with the air and fuel mixture. If for instance the cable has broken, this defaults the system to full injection volume and the engine will generate smoke accordingly while running. If the control cable is misadjusted, the result can be more, or less oil than intended.
So there you have it, either the oil injection system isn't working properly, or the inner crankshaft seal(s) might be leaking.
Hopefully this is enough detail to get you pointed in the right direction.
