Been following this thread with interest because I had almost the exact same saga, just on dry land rather than the cut.
My shepherd's hut setup was plagued by the same fridge-nuking-the-inverter nonsense when I was running AGM. That compressor startup surge is absolutely brutal — caught me off guard every single time, usually at the worst possible moment. Swapped over to a 200Ah Fogstar Drift lithium last spring and the difference was genuinely night and day. The battery doesn't flinch at the inrush current anymore, whereas the AGMs were effectively sagging on voltage the moment anything demanding kicked in.
What I've found is that lithium's flat discharge curve does most of the heavy lifting here. AGMs rolling down to 11.8V under load gives your inverter next to nothing to work with — lithium sits solid at 13V+ through most of its usable capacity, so the inverter never sees that horrible brown-out moment.
For anyone still on the fence about the switch — the fridge stability alone probably justifies it if you're running a compressor unit full-time.
One question for you narrowboaters though — how are you finding lithium with your alternator setup? That's the bit I've read is trickier on boats, where you can't just bolt on a DC-DC charger and call it done without checking your engine hours and alternator temperature. Curious whether you've gone with a Victron Orion or something else to protect the alternator from the lithium gobbling charge too aggressively.
The EV charging side of my life has made me fairly obsessive about charge rates and battery management, so I'd love to know what your BMS is doing during bulk charge on the engine.