So looks like AA has (quietly?) begun its/matched CO's summer fare sale.
Fare code basis IRT2AA3 (expertflyer) or IRT2WEB (AA.com)
Appears ~$2000 and under fares only valid from NYC (presumably the CO match). DFW/ORD in the $2500+ range.

I am seeing (all round-trip, tax extra):
$1618 JFK-BRU
$1818 JFK-LHR, CDG, ZRH
$2018 JFK-FCO

$2218 MIA-LHR, CDG, MAD

Fares look bookable at AA.com

Basic rules: 30-day advance purchase, Sat night stay requirement, $300 change fee, valid 1-Jul thru 2-Sep

Happy traveling!