I'd have thought the carbon mast is carefully designed to flex in a certain way, and a certain amoount under loading. Certainly that's the best way to use carbon. The problem you'll likely have is a difference in the flexing between the wood and the carbon.

If you glue the two together, you'll be putting the glue under stress each time it flexs. If they are seperate, then you have one moving over the other, possibly abrading the carbon. You may also end up causing a "hard point" in the bend characteristic of the carbon mast that would quickly weaken it.
You'll also be adding lots of weight at a large rotational moment that is not needed.

I'd go with the paint, or possibly very thin laminates - 1 or 2mm thick.

If you're going for inch thick Douglas fir, you're most of the way to a wooden mast all in it's own right anyway! Forget about the carbon mast and just get a wooden one!