As Horace Greely once said: "Go West, young man." Try this:
DFW-LAX-LHR-LAX-DFW for 13,362 miles
Fare: $444.20 for 1/17-21/02 travel.
$0.0332/ml; $0.0166/ml PLT
Assuming the fare is the same, you can improve on this further by connecting thru JFK each way instead of taking the LAX-LHR nonstop. Adds an additional 938 miles, for a total of 14,300. Also, a DFW-LAX-MIA-LHR routing might be possible, for a grand total of 15,988 miles, but don't know what kind of fare you'd get for that.