You can do everything except the last part of the IR in the US. A number of US schools have UK CAA approval. CPL can be done in the US. You will just have to do 15 hours of IR training in the UK and the initial IR test in UK airspace. It is exactly what L3, Skyborne and CAE do with the Integrated courses, all SEP phases and multi cpl in US fair weather training bases with IR finished in the UK.