Dont be too worried about the sink,surrender issue Bill, a lot play that way ie run out of boxs you sink.

As Jonas rightly says when you fill the boxs the ship surrenders, here you can either leave the ship on the table or remove it, both are acceptable although the first is an optional rule.
The rational is, when you fill the boxs for burden, the crew are too busy trying to keep the ship afloat rather than fight and if all the crew boxs are full you just aint got enough uninjured crew to keep fighting.
Just remember the burden box only needs to have a counter in the last box to surrender not fully damaged
From the rule book

SINKING SHIPS
If a ship has a leak and it has already received two or more water damage markers, the hull might collapse and the ship may suddenly sink.
Each time the ship takes a new water damage marker beyond the second, the player must shuffle three water damage markers and one sinking marker together, and then randomly draw one of them.
— If a water damage marker is drawn, apply the water damage normally.
— If a sinking marker is drawn, the hull gives way and the ship sinks. e ship is eliminated.