LFP is double the weight.
You can either "diode-OR" the power connections, which wastes power, or do a power selector switch with contactors to drop the submerged battery from the circuit. Yes, the bms gets complicated - you may need two. Or you could use a pair of manual disconnects. In emergency power, should your inverter care what the BMS thinks? Arguably, you'd want to ignore the bms and toast the pack by overdischarging it if you HAD to get her to land.
In theory, if you used lead bolts for the bus bar connections, or a low melt alloy, it could self disconnect at the drop passively from the heat, maybe suspend the pack by those connections? But - that same system could strand you.
This is also not without risk - you'll make a lot of hydrogen with the electrically live, burning, cells dropping into seawater (explosion risk), though dropping the battery case in might not melt the case but won't cool the cells so it'll keep burning. In rough (anything but glass) seas, the vented case will still flood and sink.
It's a silly thought-exercise, which is ok. Creativity is a muscle that needs exercise.
Your main concern, imo, should be keeping the vessel afloat and sharks starved, not maintaining propulsion, so my vote is jettison a burning pack (this is unlikely to happen, but...can) and maybe do it so the jettisoned battery case "icebergs" to where you can maybe salvage it after the fireworks are done and also not be labeled an eco-terrorist for its sinking by West Coast hippies who hate fossilfuels and also hate hydro dams, wind turbines, solar, and "toxic" lithium batteries - build a pedaled hydrofoil to make the granola munchers happy 😂.