I try to give out one kori a piece to each of my sons and family name clan members, then raise my sons up to 5 a piece and my family clan members up to 5 a piece. After that I will start handing out to non-family clan members. This ensures that the kori are upgraded as fast as possible, then that each Kukojin will have enough titles to amass a large enough income to go above the cap and start paying into the Clan coffers in a large amount.
Some time along that line you will find you have enough cash to build a theatre in every province of your direct demense. I like to directly hold 7 kori with a theatre in each at this point and let my vassals put down any rebellions that stem from the +4 revolt risk.