this idea cannot be implemented with AMX-13 but can be implemented with Tempest/Centurion. The difference is that the main gun is stabilised in 3 axis. That's why when the tank is driving cross country over rough terrain, the gun will remain on target at all time. The pitch and roll of the sea is no problem for the gun to handle. As for the recoil, most of the recoil energy is absorbed by the various systems in the tank like recuperators, and such. Its also possible to install a low pressure 105 mm gun on a tank with will give much less recoil, but u give up range and accuracy. Good tanks handle recoil well, otherwise the crew inside will be rattled to death after a few rounds. If u look at the picture, u can see that the deck of the ship has been reinforced to handle the weight of the armour vehicles. And yes, its only direct fire, but still, if you sail this sucker into an invasion fleet, u could wreak havoc on the landing craft and LSTs. U can also see from the picture that the tanks are tied down. In theory, u can strip a Centurion of its engine and transmission, and even tracks. It will weight 15 tons less and have a crane winch it on to the deck. U can increase ammo load at the same time.
this is a quick cost effective way to get a mobile seaborn fire support base. Also, u can shoot ATGWs like TOW from a ship too.