BA is not kindly disposed to hidden city ticketing fraud (where the final segment is intentionally not flown). Thus, it will not short-check your luggage.

US agents know this, are trained, have heard every story in the book, and could care less.

Thus: xLGW, later date, or nothing checked.

You could also have your bags checked through on a final segment xLHR and come up with a story about your aunt's dog being taken ill or somesuch and hope that your bag is pulled as it is required to be. If it is, you will have it at some point in the day. If it slips through, you are off to your EU "destination" notwithstanding the sick dog.