mmxbreaks

Try this:



and it should give you something like this to select:



The price is good, but there are some snags:
1. You'll need to position to Bucharest the day before and pay for overnight accommodation. Still, cheap city, that's unlikely to be a problem at a weekend.
2. The LAX arrival time means a horrid short overnight stop, so you may wish to purchase a hotel - but that'll only get you around 3hrs sleep by the time you're there.
3. Of course, there's the small fact you'll end up arriving in PHX, not LAX, the next day - so that's another cost to get back to LAX.

Nonetheless, with all that said, and otherwise workable connection times, it's a relative bargain really. LHR-LAX direct in business is closer to £5Kpp. The above I think you could do for £1,600pp including hotels and positioning flights.

Others can advise on Travel Agents that can book such an itinerary. I've used Propeller twice now and it's always worked out well, even with complex things such as this. The people there seem to understand our odd routings... Or phone the airline direct (think that price is with AA, BA is about £25 more - by which time the TA route may just be easier).

G'luck.