I also make my ice between trips. I use (used) one gallon freezer ziplock bags that I wash to freeze the ice into 1 gallon blocks, which last longer then the bagged ice. I have thought about doing just what you are considering! I didn't save the recipe for adding salt to make salt ice, but it was found online and is easy to do. You might be surprised on just how much salt you have to add though?
Here is why I didn't pursue that. I carry 296 gallons of fuel along with a generator, basically only used to heat the water in the hot water tank. I don't use paper plates (don't like the trash or bags associated with that). I carry bottled water to drink. The only thing I ever run short of between refueling - is none other than fresh water for dishes and showers. Hence, my CLEAN thawed out 1 gallon bags of water find their way to my water tank for dishes and showers! No, I don't use that not so clean water out out of the cooler!
First, I have a small onboard freezer, so I do have the ability to make and/or re-freeze some small amount of ice as it melts. My trips are usually a week and is well beyond the limits of fresh water ice (including block). Usually end up with just a cooler of cold water.
I carry two coolers, one (smaller) is for food and drink, the other (larger) is for "cleaned" fish. I also have two very large built-in insulated fish boxes, which both have water plugs and actually set below the water line. Pull the plug and they will fill up with fresh nice cool seawater, also makes cleaning them out very easy. One box is used for the catch - freshly caught fish goes there and is bleed and gilled right in the box. The other is used for the salt ice. Works just as good as any cooler and is great. Catch fish, put in fish box, bleed and gill. Clean fish on the large cleaning table on the stern, bag them, put in fish cooler, cover fish in layers with salt ice, as added to fish cooler. The salt water ice box is only opened when ice is needed to cover fish.
Clean up at end of day is actually easy - Pull plug in fish box and clean all blood and gills out of that box, pump water out. Use raw water wash down pump to rinse blood off deck, stern, and engines.