I know of no elegant solution.
Years ago there was a solid state (Pelitier) water cooled unit from Scandinavia that just didn't have the capacity for this climate.
If it had it would be perfect. It had the solid state chip in a through hull and the heat from the fridge was conducted from a aluminum heatsink (coldplate) in the box through a massive copper braid to the through hull. It was energy efficient but could only cool to a 28 degree drop from the water temp-
I used to rob the ice machine at Trump Marina's Casino hotel and that was satisfactory. I had no problem taking ice from Donald Trump. Today I'd likely take the MACHINE-
Now I make my own block ice in a chest freezer at home. It is far better than manufactured block ice we have in S. Jersey coastal area. We have one ice supplier and the blocks seem to be reconstituted cubes- It has little value.
I use several sized plastic containers and I have a dedicated block ice cooler. The schlep from car to boat isn't too bad and the ice lasts several days if the items are already cold.
There IS opportunity to increase the insulation in the engine compartment. Remove the water tank manifold and install regular home sheathing insulation. Cut holes for plywood backing plates to mount the tank manifold and follow up with polished aluminum to reflect the engine heat. I made this upgrade many years ago and really does make a difference.
You could also destroy the existing icebox interior, install new insulation and re-glass it. Who really needs the cavernous size of our 323 iceboxes (although when I bought the boat I was pleased fitting FOUR cases of canned beer in that box).
I watch a cruising show and the sailors have a 40' aluminum boat. They had an upright Norcold looking icebox that would be comfortable in a motorhome. It was worthless offshore and everything fell out upon opening the door on a port tack!
They ripped out the home-style box and made a cubbord. To replace the fridge they bought a marine top-loading box and installed it as a bench seat infront of the nav station. It looks far better than it sounds and that is because the captain is a carpenter/cabinetmaker. Here's the link- but I'm not sure where it would fit.
https://www.defender.com/product.jsp?name=dometic-cf-80-coolfreeze-portable-refrigerator-freezer&path=-1|2276204|2276226|2276228&id=680814
If I had known I'd have my 323 25 years I might have attacked the built in box years ago.
I think a massive rebuild of the existing space within the original footprint and a good engine driven holding plate would work best.
I have a friend with two holding plates in his 37' Crelock. One is engine driven for jaunts to Hawaii and the other is 12v for dockside- They take up so much room in his box a 12 pack of cans is about all that fits!
I think a trip to the boat shows and a study of what the mainstream (for easy parts and service) builders are using might inspire you.
Meantime- you're welcome to an ICE COLD Stella from my homemade block ice!