I understand what you are trying to achieve.
But solid carbon rods will only help reduce the bending moment over the mast length. Also laying the rods into a core (wood) , you will have a lot of shear between the two dissimilar materials.
My thoughts on rapping.
I have attempted this many years ago on a bike frame.
I found it was extremely hard to get the core profile correct, meaning after wrapping it always end up oversize and profile lost.
Sanding is the only solution to maintain what original shape you started with. The only problem with sanding is you remove all of those fibres.
Just my experience.
But your question how much is enough.
If you use 300 gsm uni carbon and 600gsm double bias +-45deg lay up this.
3x uni first
2x double bias.
Last layer of laminate, 150gsm twill. The twill is only a protection layer.
This would be a start, but personally it will not be stiff enough in torsion.
The question is how are you going to do the laminate.
I can give you some ideas if you are interested.