Swift Trawler 34 Water Problems

How deep are we talking. Sounds like a lot. You definitely shouldn't get enough water to float battery boxes. You need to start doing a very complete inspection to determine where this water is coming in. If you determine the leak is not happening at rest, my next guess would be shaft seals that are only leaking under way.

Had a good bug like this years ago.
Exterior trim from the transom swim platform continued forward up the hull sides for 4-5 feet.
It also served as an additional hull side rub rail.
At rest all is good.
In a sea, water would enter the bilges where the trim was bolted to the hull.
When we looked under this trim, the factory caulk was missing. It was also a poor factory fit and assembly.

What's low on your hull sides?
Vents, trim rails or a thru hull with a bad hose behind it?
Swim platform or ladder thru bolt?

With power off, wash out the box with WD-40 and let dry for a day. If you have old relays in there try to remove the covers and wash again with WD-40.
Good luck

+1 on WD 40. Also, a remedy that sometimes work, sometimes not, is, after perhaps flushing device w. fresh water and WD 40 - put it in a couple of plastic bags or a can/jar/bucket filled with dry unboiled white rice for a day or so (!). Make sure there is no contact with outer air using tape or rubberbands - the rice might, just might, "suck" the remaining humidity out of Your Black box. Won´t hurt to try + it´s super cheap - sure helped me save a few cell phones (don´t ask).

You probably want to use fresh water before WD40. The fresh water will dissolve any salt. Then maybe distilled water. Basically, you need to get the salt off the electronics otherwise it will corrode away.

To get the water out, you can use isopropyl alcohol. It will remove the water.

Once you have everything as clean as possible, let it dry for 24 hrs or so. You can also stick it in an oven on LOW ( < 150 deg F ).