The existing name host should be able to point the name at the Bravenet site. The whole point of domain names is that the address is portable.
If you use a PC based editor you can upload the files to wherever you like. The Wizard just isn't designed to work like that.
If I was your client I would be very upset about the site being on your account. I would expect a separate account that could be handed to me in its entirity if I decided to use a different developer (or you decided to pull out).