I got another idea for you... mix some hollow rubber balls into the concrete mix. Yes, it will reduce the structural strength a little bit, but it should also reduce the weight of the ship without changing the displacement or the permeability.
I’m no engineer, but my intuition says reducing the diameter of the balls would also reduce how much they affect the structural integrity.
There is a type of concrete called AAC - Autoclaved Aerated Concrete. It is made by adding powder (aluminum I believe) to the mix and causes the concrete to create air bubbles. This type of concrete naturally floats.