One thing missing is the energy cost of removing/drying the carbon flakes from the system, then moving themfor combustion. In a closed loop, you could create a cycle that consumed co2 and reconstituted it by burning and reproducing co2, but it would taper off. Yes, you could burn the carbon flakes to produce more energy than the system consumes, but you'll need more oxygen from the environment to maintain the reaction. At 92% efficiency, you'd run out of oxygen to maintain combustion after a dozen cycles or so, in a closed system. With an endless amount of atmospheric co2, the picture changes.
2460 kwh, at 12 cents per kwh, translates to $295 of electricity per ton. It optimally produces twice as much as it consumes.
Maybe a Stirling engine that uses a belt feeder, with the flakes skimmed from the catalytic reaction chamber onto the belt, drying in the heat of combustion, then dropped into the burner, and the exhaust bubbled back into the solvent. Then it could deposit the excess flakes while producing power by directly consuming co2?
This is pretty phenomenal, edging into the "too good to be true" domain.
Anyway, pointing out that pure carbon can be burned is good thinking.