If you do not have an owner's manual, you can download one for free from this link to Honda
http://marine.honda.com/support/manuals/models/BF90EFI
Choose the right one by your frame serial number.
The storage section takes you through a step by step of how to store the motor.
In addition to changing engine oil, filter and gearlube, etc, you run the engine on stabilized fuel, run the engine out of fuel, and drain the carburetors. Then remove the spark plugs and shoot some oil into each cylinder and rotate the engine a couple of times. No fogging....like the two strokes.
There are alternatives by running the engine on an oil/stabilizer/fuel mixture for a short time. You can probably google for various mixtures.
In the end, you should still drain all of the carburetors.
I doubt that fogging through the carb balance ports will be very effective. I do not think that you can take all the screws out and still run the engine. If you unscrew them one at a time and shoot oil into it, by the time you get to the next one, the first cylinder would have burnt all the oil off.
Be sure to store the engine in a vertical position to be sure to prevent water from accumulating in the exhaust.
Mike