Nock - I've tried several methods to raise queens.
The method you mention - works, usually. I used this route for 4 years.
However, I found (this year) what I personally think is a better approach. I pull the queen, some capped brood, stores, and some nurse bees, out of a strong hive and into a Nuc. Then I let the strong hive make QC'S. After the QC'S are capped, I transfer them to new hives, and reintroduce (via newspaper combine) the original queen. I get more qc's this way, and the queens seem to be higher quality. Fwiw.