Booth carbon and fiberglass work well with wood. But carbon is so stiff it mostly does not share the load, so you end up paying a lot for the carbon while being stuck with the weight of the wood. One way is to use just a little carbon on the inside, so that the bike is mostly wood, and before a load would be such as to break or deflect the wood, it goes to the carbon. But doing that requires real engineering. Carbon is a difficult material to design with. Most people don't understand it.
Glass allows you to overlay wood and share strength and stiffness. You should mostly design for the wood to do the work, and use only glass cloth and fiber to the extent required to make the joints strong or provide waterproofness and mild knock resistance. Say 4 oz glass. As you know there are plans on the net for ply recumbent, I don't think they use fiber, but hardware for the joints, but there are lots of blogs on bonding to bamboo with everything from hemp to carbon.
Something to read about is hardware bonding, where studs are bonded to wood. A very cheap and effective technique.
For all this stuff epoxy resin is the go to resin, and may be a little difficult to get. There are lots of boatbuilder making wood epoxy boats in the P. though I realize it is an extensive area.