If you can find an AA metal flight for the transatlantic portion then connecting in LHR isn't as costly. It's the flights on BA that have the fuel surcharge/ripoff.

Although its not searchable online via AA.com, you can also use miles on Iberia and Air Berlin to get to Europe.

And, you're also just up against AA really cutting back on lower level/cost award availability.

From JFK I think you can also get to FCO, MAN, & DUB direct on AA, but those may be seasonal.