This is just a guess since I'm not familiar with your boat but why not? If the battery location is secured and out of the elements I don't see an issue. Hopefully someone that knows your boat can chime in with a real educated answer.
while the motor is running can you hold your hand up, or a piece of paper, in front of the smoke/steam? maybe that way you can tell if it's steam or oil burning.
I have no idea what's in the ECU but I'm absolutely guessing the problem may be either a cold solder joint or break in a trace on the circuit board. That's why things change when you press on it. Thanks for posting this.
I've had several sized aluminum boats in my life and blame them on my messed up back. They are nice and light for towing and the low maintenance but you get your ass kicked, and back pounded when the wind blows and conditions get rough.
Is the gas tank vent clear? Loosen the gas cap next time it happens. Do you have another gas tank you can tempy run it on? Is the primer bulb hard or deflated when the motor bogs down? Have you checked, cleaned or replace any fuel filters?
We all have something in common that makes people interested in each others issues and desire to help. It's called a love/hate relationship with boats.
dingbat has a good question "Is the winch cable taunt while backing into the water" Try giving the cable/strap a few feet of slack it may help the boat float but still secured to the trailer.
I expected your transom looked like that. My boat has the same type of cut out transom but doesn't take on water while launching. I'm guessing your ramp is steep, maybe you may be backing in too fast. Are the batteries and fuel filter getting soaked?