£224 or approx $358 is the outbound part of the current O fare quoted for JFK-LHR return on aa.com (composed of half the O fare: $105, half the YR: $229, and the taxes ex JFK: $24).
$1723 could have been quoted as a one way fare JFK-LHR (i.e. much higher than half the return fare).
If the outbound part of a return had been quoted of $1723, it would have been based on a roundtrip fare of 2 x (1723 - 229 - 24) = 2940. According to EF, there is currently no AA fare of exactly $2940 (although there are some Y fares around that price).
While availability in particular fare classes quite often varies between markets, I doubt that AA has different base fares in different markets (EF can show the base fares for the US and UK markets).
The easiest way to compare available fares in the different markets (i.e. determined by the base fare and availability in the fare class) is to change the "country of Residence" on the aa.com reservations page. EF is a convenient way to find availability in the different fare classes in the US and UK markets.