A few months ago I've registered IBC in Belize. It has bank account in Latvia, Rietumu bank. This company hasn't processed any transactions yet. I think it could be used as a Holding company in yours suggested structure.
Most often there is nothing wrong to do it the way you have done it. Many have a company that they don't use and later use as Holding company.I went further with the process and used it as a Holding company for my other offshore corps. no problems at all "it's just do it" no question asked.