What you're telling us is all based on your educated guesses as to how they might have pulled this. There are things that feel a bit weird and I'm guessing you have no evidence to prove them, such as the scammer shipping the real SIM back to Atlanta in time before you realise the issue.
How did you realise the SIM card you were handed was fake? Couldn't it be that they instead duplicated your SIM whilst you weren't looking?
IMHO the police (or FBI or whatevs) in the US should conduct the investigation as that's were the fraud happened. They'll evaluate if it's worth it contacting their counterparts in the UK to move forward. However I also think it is good that you've given a heads up to the UK local authorities.
Do you remember what company was offering the local SIMs? I've seen mostly Lebara, but not in Heathrow...