It sounds like you bought the flights from BA, but that AA is actually operating them, i.e. you're on an AA plane. (Except for the Aer Lingus part.) Is that correct?
I have a ticket from Seattle to Dublin via Heathrow (7/20) and LHR back to SEA (8/24). I bought it from AA, but BA is operating the flight, i.e, it's on BA metal. Aer Lingus is the connecting flight from LHR to DUB.
It looks like our reservations are opposite sides of the same coin. I'm thinking my flights may be in greater jeopardy than yours since mine are on actual BA planes. But who knows how these partner airline things work in this kind of a situation?
Is BA the boss of Heathrow? I wonder how a BA strike would affect AA or Aer Lingus planes and crews?