For honey production you must manage the colony in such a way that don't swarm and take away your work force. I would bet you are right at your swarm season and bees are hard to stop from swarming if they have made up their minds. A lot of the actions to prevent swarming probably should have happened already.
If you are running two brood boxes, tilt the upper one up one end and see if you have queen cells with larvae in them or sealed ones. If you see sealed ones, the queen may have already left with a swarm. If you run a single brood box, look at the bottom of that box for the same thing. That or by frame side bars is where swarm cells are almost always built. If you are an sbb user the swarm cells may be higher up on the frames at the bottom of where the bees can heat brood comb.
If you are fortunate and the bees have not yet started raising queens, then you can place a foundationless frame on each side of the brood nest to employ the young bees and help relieve the congestion in the brood nest that promotes swarming. Since you mentioned checkerboarding, I assume you know why it is done and suggest you do it. It is done with drawn comb if you have it. If you don't have drawn comb, I would put foundation frames between capped frames of brood and throw on a super so the bees have places to be rather than congesting the colony.
Then, every 9 days. Tilt that brood box and look for occupied swarm cells. IF you find them, chances are the bees have made up there mind already. At that point I split the colony at least three ways and stack them all on the same stand with either plywood divisions or double screens. My objective is to at least cut my losses. When they have raised new queens and the old ones colony have got over swarming, just remove the divisions and let them sort it out. You will almost certainly get requeened with the survivor genetics that were good enough to come thru winter and be strong enough to want to reproduce and you will have the full population to store honey instead of stocking a tree.
For less long winded and more cogent explanation, go to Mr. Bush's website and read his material.