I don't have names for you but my dealer replaced the transmission with no fuss. Actually, they told me the fix was to go into the transmission to do something but they were simply going to swap it.

They did advise me it may take longer than usual since this was the first XF they worked on. 48 hours later it's ready ...but I couldn't pick it up yesterday before they closed.

I think the problem is your dealer and you may have to locate a more customer-friendly bunch of people.