AA Vacations to Europe was* giving 20,000 bonus miles (+ their regular 1,000 bonus) to select cities--so if you book these, the extra bonuses can help offset the SAVER-ANYTIME difference. [I've done 3 plus one more in November, 4 x 21,000 + RDMs, make ANYTIME more bearable.] BUT, nothing will soften the removal of n/s between JFK and Europe.
*this may still be in effect(?)