David LaFerney - You're right - more bees in that 5-framer are in order. Think BEE FOUNTAIN, not Cell Starter. Michael Plamer call his "Bee Bombs". Ever seen 3 inches of bees pile out over the top bars and beard over the entire box so you can't see it?
Challenger - Try using at least 2 deeps or 3 mediums instead of a 5-framer for your Queen Cell maker colony. The average results go up a fair bit. How does 152 lbs of overfed nurse bees + food sound? Yup, they can make some QC's awright!
So, early in the season, combine two colonies with the newspaper method, making sure the bottom colony is stronger, and pull the queen out of the top colony. Give them a week to get acquainted and happy. Now place queen excluders between each box so you can easily find the queen. This should be 3 or 4 boxes tall, you could even repeat this with a 3rd, smaller colony to get 4 boxes tall. This big colony will be your Cell Starter/Finisher colony.
10 days before grafting (Day , go through the colony and REMOVE ALL QUEEN CELLS. Make sure the queen is below a queen excluder or a Cloake Board in the bottom box (you should now remove the other excluders). You can remove any open honey comb that is hatched out or has been back-filled with honey and replace it with imported capped brood.
5 days before grafting (Day 6), begin feeding the Starter/Finisher - Pollen patty, 1:1 sugar syrup with HBH.
At 7 AM three days (Day 8) before grafting (Grafting is on the afternoon of the Day 11, the 4th day of isolation), isolate the Breeder Queen (not the Starter/Finisher queen, but the one you want to make new queens from - perhaps one whose daughter workers display hygenic traits) onto 3 frames of new, open comb contained in a hive partition made of queen excluder material.
At 7 AM on the Day 11, go through the Cell Starter/Finisher colony frame-by-frame and REMOVE EVERY QUEEN CELL (you can use these to make nucs if you like their queen mother's genetics). Slide in the Cloake Board or remove the queen entirely, placing her box behind the hive and facing the other way. You will be crowding 4 boxes of bees into 3 boxes, keeping the capped brood and eliminating everything else, except as folllows: the 3rd box is the one that will have the grafts. It gets a 2-gallon feeder, a honey frame, capped brood, pollen, a gap for the grafts, pollen, capped brood, (1 more capped brood if it fits - some feeders leave enough room, some don't). DO replenish the feeder. You can add the 4th box full of 10 imported capped brood frames if you are going to repeat the queen rearing cycle again later. Close it up and go have lunch, and set up your tent for grafting. Soak a few towels with water and put them in the dryer on low heat. Pull them out at about 2:45 PM while still damp and bag them, put them in the tent. You can also put spray bottle of warm water in the tent.
At 3 PM on Day 11, GRAFT! Take a frame of larvae (the oldest should be about 80 hours old) from the isolated Breeder Queen, carefully brush the bees off with a large feather, and blow or brush bees off your bee suit before going into the tent. Graft one bar, covering the grafted cell cups with the warm, damp towel as you work, and go place the frame into the Cell Starter/Finisher. Then go back in the tent and graft the second bar, covering the grafted cell cups as you go. When finished, go add the second bar to the queen cell frame in the Starter/Finisher. If using deep boxes and your queen cell frame has 3 bars, graft the 3rd bar in the same manner and add it to the frame as you did the second. Try to work quickly - a bar should take less than 10 minutes to graft and place into the Starter/Finisher.
In the peak of the season, a rig like this should easily raise about 100 queen cells - I've run a 5-deep tall Starter/Finisher with 2 Cell Builder boxes with 2 frames of 32 cells each in them, with all but 3 grafts made into queen cells.
Let's give credit to the gurus - Michael Palmer, Kirk Webster, and Brother Adam, whose method this is (OK they vary somewhat, but this is Brother Adam's idea with some modifications) and a nod to New Zealander, Harry Cloake if you are using a Cloake Board. :applause: