I seem to think that anything supplemented with oxygen will be better than the non oxygen alternative. Add to that the fact that you've got movement, and no dead spots, and i find it hard to believe the k1 isn't better.
Compare lava rock with supplemented oxygen via an oxygen reactor before the canister, then you've got a fair comparison. However, lack of movement in the lava rock makes me think dead spots are unavoidable without movement.
I think that simply having k1 in a canister with no trays to separate space and an oxygen reactor before the filter to diffuse oxygen into the water would be the best option. You get turbulence in the filter allowing for movement, you get the added benefit of oxygen, and it's outside the tank with no added equipment.
In the videos linked earlier for the k1 "bottles" the airstone provided both movement and oxygen. Why not use the canister 'pull' for the movement, and diffuse oxygen for well... the oxygen?