So according to wikipedia, the Sea of Galilee is 13mi by 8mi. It's a lake. A big, but not very big one. Generally you wouldn't get ships on a lake that size, large boats sure, but not ships. Those boats generally don't need a lot of ballast, particularly because you are't going to get really large waves on a body of water that small. Even if you did, does it even make sense to move ballast stones down to the shore, then put them on a boat across this small of a distance, just to dump them, when in the same amount of time you could probably just load up a mule/horse/camel train and walk around the lake, and for better profit than pulling down the stones. (Note there is lots of historical evidence for trade by boat on the sea, I'm just not convinced of the need for ballast stones, and there is nothing on one side of the lake or the other that suggests an empty return voyage even makes sense).
Some other problems with this theory:
1) Ballast piles from wrecks are much much smaller than 50 meters by 50 meters, and not 5m high.
2) dumping ballast stones wouldn't occur in such a well confined way resembling a pile - there would be more outlying boulders, potentially increasing in density towards a central spot (the designated dump spot) rather than a pile with edges like this.
3) 4000 years ago, it is not clear to me that there were ships with the right properties to need balast stones anywhere. I'll be glad to be shown wrong, it's interesting. Similarly, trading in ancient times like this was usually far more circuit based than "there and back", so you get and drop items every stop.