Personally I would ask the Turbo specialist if they can rebuild the turbo (which they will normally give a warranty) if they can't rebuild it then buy a Turbo it will very likely come with a warrantee of it's own.
My own X5 E70 was brought at a silly low spares or repair price due to Turbo issues I fitted a Rebuilt Turbo (cost £460 with fitting kit) along with a New actuator that lot was purchased with a 2 year Warranty, 4 years and 30k later still going strong
So as BMW are unprepared to give you any support why give them your money?? I would move the car to an Independent Garage also get the original Turbo back (why Northampton ?) If you talked to someone like GAP Turbo Chargers in Bristol I am sure they will collect your car fix it for a sensible cost and you will have a Warranted repair that will be supported.
That would be my course of action for what it is worth
Dave