some futher North America alternatives:

As proposed:
...LAX-DFW-ANC-DFW-PHX-LHR...13,459 miles (if your dates correspond to ANC flights)
...LAX-DFW-SEA-DFW-PHX-LHR...10,693 miles (proposed SEA replacement)

Other possibilities:
...LAX-DFW-MEX-YVR-MEX-LHR...12,608 miles (alternate version, with JL on MEX-YVR-MEX)
...LAX-ORD-MEX-YVR-MEX-LHR...13,868 miles (slightly longer alternate version, transiting ORD instead of DFW)

caveats:

1) JL-flights YVR-MEX only operate twice a week (but will have much better comfort and service than an AA-757 to ANC or SEA)
2) ORD-MEX seems to be a seaonal flight. DFW-MEX operates year round.
3) I didn't check to see if MEX-LHR has F, though I suppose it must.