Why not just wrap carbon around the core, which might be some light weight material like paulownia or even foam? Using UD straight and at 45 degrees should be effective, perhaps one layer of weave for the surface, for aesthetics if not else. Carbon weave tube is perhaps the best solution, but more expensive than using fabrics.
If some structural complications is wanted I would divide the core in three parts, wrap them individually in carbon and then glue them together in vacuum. Then more layers of carbon on top, so three hollow beams side by side would be a core. Brokite uses that kind of method in their carbon twintips.
Simplest way to add stiffness is of course to add thickness to the mast. Thickness (and chord) can be bigger near the board, there added stiffness is needed and increased drag does not matter.
I don't see why a carbon rod should be at LE. I-beam is also structurally suspicious if it is made thin parts. Hollow beam is much better in that respect and for sure easier to make.