They don't want to change in the US...
Changing planes at LHR is bad enough. Changing planes and airlines and terminals is just asking for trouble IMHO.

I'd go with KL (if cost is a consideration and a Z-class or similar can be found) or LX (if KL is no cheaper or if first class is required).
There's also a new LAX service on the AZ 777 (via FCO), which may be worth looking at if the price is right (the 777 is a lot better than other AZ products and has no middle seats in biz).