From Isaiah 33:23 "Your ship’s tackle hangs slack; it cannot hold the base of its mast firmly, nor spread out the sail."
The phrase "cannot hold the base of its mast firmly" is evocative. The frame of a trireme was flexible enough to demand a strong cable connecting the back to the front--a strange kind of keel. If you want the mast to stay put, and it can't be tightly held by its socket, maybe cables fore and aft connecting to the prow and stern would give enough downward force to keep it in place. You really want three points instead of just two--maybe port and starboard cables at the same position as the mast would suffice. The connection of the mast socket to the frame of the boat has to be very strong, so I'd guess there'd be something solid to attach to at the side of the boat. Or maybe the socket was deemed good enough to constrain side-to-side motion of the mast, so long as it could be held in it.
Such cables would help spread the force from the sails to the back of the boat as well as the middle, and in bad weather keep the mast from coming loose. Of course the downward force would tend to bend the boat, demanding an even stronger tensioning rope (hypozomata) to counteract that.