Unfortunately, this is a problem with modern engines
The technicians rely on the car's computers to tell them what's wrong.
They should have down-loaded the engine's run log to see what data the sensors were outputting when it dropped power. That should direct them to the fault or faulty component.
BMW did have some issues with twin spool Turbo's low end spool shattering recently. This can mimic a 3 pot feel as the engine goes into limp mode. For some reason that cannot be fully explained, it usually happens just after you stop and fill up.
I know three poeple here in Aus that this has happen to recently.
In regard to costs, speak to their Operations manager at the dealer where you are to see if BMW will pay for flights to and from home for you. They should be able to arrange to have a loan car made available from your BMW dealer near home. They usually prefer this as it keeps their costs internal with the dealers.
I hope this helps you