Christa I don't think it will take long at all. Unless Josie is incredibly upset by this tiny invasion then I think you will feel comfortable about it very soon. Just remember that Brodie is going to take a few smacks and he will have to learn a few lessons from Josie but he will survive. I think Josie is going to be happy with a little playmate and I think your worst problem may be that she is a little to rough with him. It will scare you more than hurt him.
Rosco fit in with all my big ones so quickly that I had no fear leaving him out within a short few days. Abigail was so weak that I was afraid she would get hurt and I kept her caged during the day longer than Rosco. Finally I just held my breath, left her out and went to work, worried all day every day for a week or two, then realized that everyone was fine and never looked back. You will know when its safe and okay to leave him free. You may worry and there may be a few tiny issues but I have no doubt that you will know when the time is right.
You are going to have so much fun when they become buds!!