I last saw this airframe in a museum in Florida when the restoration had just started. It certainly seemed to be fairly complete at that stage. As for displaying it in the UK didn’t Lindbergh specify his requirements with Miles and then used it widely throughout Europe? Seems a good enough reason to display it here to me. Might be nice to loan it to Old Warden at some stage though?
The picture you reference Ollie, looks just like the Bf/Me 109 diorama in the Battle of Britain exhibition at Duxford. I fear, judging by the bent prop, that he will have to have the engine shock-load tested and that won’t be quick or cheap.