If I understand you right, you are using the Cloake Board differently than it was designed. It doesn't matter which hive you get the eggs (actually larva) from. It doesn't need to be the Cloake Board hive. The Cloake Board hive is where you put your grafts. The day before you graft you slide the divider in to make the top queenless. There needs to be nurse bees up there (the entire instructions are longer than I have time for right now).
So the next day after sliding the divider in, you graft from any hive that you want and insert the grafts into the Cloake Board hive. The queenless half that you added the grafts will start the queen cells. The next day you can remove the divider to make the hive queenright again.
So the next day after sliding the divider in, you graft from any hive that you want and insert the grafts into the Cloake Board hive. The queenless half that you added the grafts will start the queen cells. The next day you can remove the divider to make the hive queenright again.