IO540,
Your post is pretty much what I was getting at.
I know of at least 3 ppl that imported aircraft without an export CofA. They were refused a CofA by the CAA.
One guy couldn't get an export CofA because the aircraft was damaged, he bought it repaired it IAW the manufaturers MM then applied for a CofA. The CAA refused.
In the end he had to register it with the FAA, get it certified, apply for an export CofA. Then re-apply for a UK CofA.
I think he left it on the FAA register in the end.
Another person imported a homebuilt aircraft from the USA, he was told that unless he could verify the standard of all parts and materials he would have to replace them. I think the aircraft became a toy for the local children.
I am not sure about a second hand engine but would imagine you would have difficulty convincing the surveyor of its airworthiness without an overhaul or export CofA.