I know the carbon stays are purportedly for damping vibrations.

I mentioned Al and most metals/alloys are isotropic, meaning same properties in every direction. CF composite is "anisotropic", meaning different properties in different planes. Largely due to the fact that the fibers are oriented in a selected, deliberate arrangement. Then stresses to the frame in a direction that place the fibers in pure tension will yield the stiffest behavior, whereas stresses in transverse directions may allow more flex. I haven't studied the vibration damping properties of CF, but my guess is the anisotropic nature of the composite is largely responsible for their ability to absorb vibration. Another possibility is that the relatively soft and flexible plastic resin matrix dampens those vibrations, because the vibrations have low enough amplitude that they are not significantly stressing the carbon fibers, and the vibration damping properties of the matrix itself may dominate in that realm.