Consider the other side of it.

Suppose we don't make for a station.

Schillingschen reports us dead.

Nobody looks for us--unless perhaps out on the lake for a hat or some scrap of clothing by way of corroborative evidence.

Suppose we paddle out of this gulf and take to shore somewhere along the north end of the lake.
We've no food, no tents, only one gun, next to no ammunition, nothing but money and a purpose.