Okay - found the rules.

Your change fee is only 50 pounds. The stopover is free enroute to final destination. However, connecting flight/s is subject to availability.

PENALTY - CANCELLATIONS BEFORE DEPARTURE CHARGE 50 PERCENT AFTER DEPARTURE TKT IS NONREFUNDABLE WAIVED FOR DEATH OF PASSENGER OF FAMILY MEMBER CHANGES ANYTIME. CHARGE GBP 50 PER TICKET WAIVED FOR UPGRADE TO HIGHER FARE. NOTE - RESERVATION CAN BE CHANGED ONCE AT A CHARGE OF GBP 50. MAY UPGRADE ENTIRE JOURNEY TO HIGHER FARE WITHOUT PENALTY.

You may have the ticket reissued either in UK or in USA. My suggestion is getting it done in the UK at Heathrow.
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DAY/TIME - APPLIES AT ANY TIME MON-THU ON INTL SECTOR. DAY/TIME IS BASED ON TRIP DATE OF INTL SECTOR.

All travel dates must be on weekdays only.
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STOPOVERS - UNLIMITED FREE STOPOVERS ARE PERMITTED AT:
ATL/BOS/BWI/CHI/CLT/DEN/DFW/DTT/EWR/HOU/LAX/MIA/NYC/ORL/PHL/PHX/SAN/SEA/SFO/TPA/WAS, IF IN ROUTING APPLICABLE TO FARE AND UNLIMITED ADDITIONAL FREE STOPOVERS ARE PERMITTED AT LON/MAN, IF IN ROUTING APPLICABLE TO FARE. A STOPOVER OCCURS WHEN THE PASSENGER DOES NOT DEPART AN INTERMEDIATE POINT WITHIN 24 HOURS.

Which actually means that you may connect to your final destination from any of BA's US gateways.
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As you did not provide us with your date of departure, I can only guess it's around September? Based on the above fare basis, the fare should be around 626 pounds before tax? BA/AA has a combined joint fare now that is actually lower than that at around only 436 pounds before tax. But that fare locks you in on travel dates.