Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

"All my miles are with American. It's seeming that if I use the lower mileage options, it still costs around $1200 per ticket. Is there some way to reduce the surcharge"

Yes: redeem on some carrier other than BA, which has very high surcharges for long-haul travel. The problem is that finding low-tier award space for premium-cabin TATL travel on non-BA carriers in July can be challenging. You can see in you can find anything on Air Berlin for JFK-DUS-STN (London/Stansted), and you can call AA to see if there is award space on IB for JFK-MAD-LHR, or award space on 9W for EWR-BRU or YYZ-BRU (with a connecting flight on AA from LGA/JFK to YYZ). From BRU, you can take the train to/from LON or PAR, but the train costs money too.

The aa.com website cannot display award-seat availability for IB or 9W; that's why you have to call AA.