DUB to the US via LHR on BA is ridiculously cheaper than LON to the US. Also Club World fares on some days and on some flights less than half of EI's business class so if you're not in a hurry it's a steal.
In fact a cheeky one would be to book via BA website. Book American going direct from Dublin to JFK, ORD, Charlotte or Philly, avail of pre-clearance and come back via LHR. If you're flexible it can be done return for only marginally more than half of EI's one way (sales excluded) price.