First, your mark is no where close to 13 miles of the coast. The water is over 300 feet deep at 13 miles.
Second, AARC is correct that 50ft would be extremely shallow for a ship during a storm. The gallons werent driven onto the shores, they were bounced on the bottom (often onto reefs) until the keels broken out from under them.
First my mark is almost exactly 13 miles offshore at 30 degrees N latitude.
Second, there is no way a 100 ton 6 gun patache could have bottomed out in a trough in 50 feet of normal water level. (Wave theory).
I assume you are talking specifically about the 1641 fleet in your last sentence. If so, Duro informs us that some foundered at sea, while others were actually smashed against "cliffs".