Yes.
Wait.
Does your car have an electric fuel pump also?
Sorry, I had to think about that for a moment, because on the race Z there isn’t a mechanical pump, only two electric pumps at the fuel cell. My stock 72 Z only has the mechanical pump, in fact the system is the original equipment from 1972, no electric pump, and no added regulator.
So if your car has both an electric and a mechanical pump, between the electric pump and the mechanical pump should be OK.
The stock mechanical pumps shouldn’t produce too much pressure, as they were designed to supply the carbs without a regulator. You might want to check the pressures in the system. That will help you understand what is happening, and why fuel is spilling out from the carb throats.
As dirty as the float bowls were, the problem may not have been too much fuel pressure, but rather dirt in the needle and seat, allowing the bowls to overfill.