It seems like it's 3-4 weeks for them to reach the recommended 2 1/2 lbs live weight. Would you just keep them in the brooder until it's time to process?
I usually put mine outside at 2 weeks if the weather is good. I can't keep a large amount of Cornish game hens in the house. This time around we plan to have them processed at 5 weeks so they will have a bit more meat on them.