I think you've gotten good advice already, but being a forum and all, I'll throw mine in as well. (Free of charge, which some might think is too high a price!)
There are several problems with the CF rod as the primary source of reinforcement. Even though it's running the length of the neck, the part supporting the break is still relatively small. It's probably strong enough, but the glue area is still relatively small and my suspicion is that with that cross section it will subject to side forces that may compromise stability. It does little to strengthen the short grain break, which is the root cause of multiple failed repairs. Full disclosure - I am a mechanical engineer, not structural...
My strong preference would be for the back strap type repair, already noted on frets.com. You'd remove the faceplate and reglue the headstock to set the alignment. Then you would thin the entire back of the headstock by the thickness of the backstrap. That would extend onto the neck shaft well past the break and be blended into the neck shape. A new faceplate would be installed, and the original logo (pearl I assume) reused. The larger glueing areas here would offer much greater support than the proposed permanent truss rod cover and short back inlay.
I think this method would support a truss rod as in the original construction, but I could live without the truss rod too. Many instruments don't have one, and a mandolin will do fine without it. The CF rod would be be helpful here, though not as the main source of strength for the broken section. I am loath to argue with Will Kimble about mandolin construction, but other builders such as Paul Newson have built several fixed-reinforced necks with great success. It's part and parcel of old Martin guitars as well. You do have to be more careful with compression fretting and such, but once the relief is correct, it's likely to stay there.
Summary - I could go either way on adjustable or fixed neck reinforcement, but believe the front and back strap repair has a far greater likelihood of success, near 100% if well executed.
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