Marine propane water heaters.

Had one on a small sailing cat, hated it. The flame was on or off so the temp went up and down. If you can find one that modulates the heat it would be a different story.

Zero experience with these in the marine environment but plenty of exposure in the RV world which is less demanding in many ways. Short version: All but the best suck. As mentioned above, all kinds of flow rate delta T issues, especially when there's long runs. Welcome to the "cold sandwich" The instructions in the Atwood version state "Navy showers are not recommended". Total PITA. The ONLY brand that I would look at is TRUMA and only if they have a true marine version.

I have had propane on a boat, but am not a fan of it. Ideally I'd be looking for a hydronic system which is electric/engine/diesel for hot water AND compartment heat. Aquahot makes one for the RV world, I believe they make marine versions. I am sure there are others. Not the cheapest, but this is not really a place to skimp.