My speculation:

Polystyrene would make your tufa lighter. Styrofoam and cement combine very well because styrofoam does not react or degrade in the corrosiveness of cement. However, it will degrade in UV light, so none of the polystyrene should be exposed to light (then again, tufa is supposed to look aged and pitted). One advantage perlite has is a very irregular surface so the mechanical bond is good where it might not be on individual polystyrene beads.

I haven't worked with it myself, but there's a building material called Panel Crete. Maybe this link will provide some info in the right direction.

Here is a link that might be useful: History of Polystyrene Concrete

Does anyone know what the large bags of polystyrene sold at the home improvement centers are used for?

The polystyrene beads are combined with some sort of adhesive or binding agent & gets injected in the walls of houses.

It is usually done on older homes to update them to be more energy efficient. It is a really neat process. I actually was thinking of getting some large garbage bags filled with this foam to serve as a base for boulders.

Polystyrene is a common lightweight aggregate. There are a couple of places that make it specifically for concrete.

Another option is to increase air entrainment, with air entraining admixtures. If I am not mistaken, aluminum powder is supposed to have a chemical reaction which causes hydrogen bubbles.