Have you checked the flight search/aggregator sites mentioned in the key posts thread?
book through continental, i did this route last year.
couldnt find one airline to complete all legs of journey though.
Why does it need to be one airline? With interlining irrespective of the airlines you choose your bag gets forwarded without you having to do anything (unless you fly via LAX!). Without, it doesn't matter whether they are the same airline or not you have to move your own bag from flight to flight... If you are staying over at each point why should it matter? FYI opodo allow multileg booking across airlines (no association).