Well, I don't know how to remove the cover from a Honda top mount control box (see my post below), but I do know something about lube technology.
The advantage of synthetic oil vs conventional oil in the automotive world is three fold:
1. Better protection under high temperature conditions because of the higher film strength and flash point.
2. Better protection under extreme low temperature conditions because of better flow characteristics.
3. Longer functional oil life because of fewer easily oxidizable components. This allows extended oil change intervals without sludge or varnish accumulation in cars and trucks.
However, these properties are not really relevant to outboard engines that run cooler than automotive engines. Extended drain intervals or not recommended for outboards because of moisture and fuel dilution issues, even by the manufacturers of synthetic oils. So if you change oil every 6-12 months, you are probably just wasting money.
There can be some advantage to using synthetic if you need to start your engine at very low temperatures or go from startup to full throttle without sufficient warmup (like tournament bass fishermen). Also a little better protection if you overheat.
But in general, there is really no reason to run synthetic oil in an outboard under normal conditions. Honda generally recommends 10W-30 oil rather than 5W-30. It contains less viscosity improver so it tends to be more shear resistant. Also, it is best to run FC-W or high mileage formula oil in outboards. They are blended to the mid to high range of 30 weight and are better able to handle higher rpm and fuel dilution. Typical automotive oils are blended to the lower end of each viscosity range for better fuel economy.