Thanks to all. We had no problem using any of the OW lounges. In particular, thanks to JDiver, who pointed out that we could use the Cathay Lounge, which we would never have thought of. Your prize is one of the AA spa bags that we took. Of course, you have to fly to the East Coast to pick it up...
A few notes of interest for those who are unfamiliar: The JFK lounge is big and the service was quite friendly. There is almost nothing to eat, however.
We missed the AA arrivals lounge due to a delay, but caught a BA Terrace Lounge on the way to EDI. Quite nice--2 levels with lots of snacks and friendly folks. Likewise, on the way back, the EDI lounge was also great. Small, but free internet and more food. The European lounges do put many of the US ones to shame.
The Cathay Lounge at LHR is nice. To get there, follow the signs in T3 to Gate 1; it's not with the rest of the lounges. At 9 am, we were the only ones there and had the place to ourselves.
Mike