I'm absolutely amazed that OP thought such a long sea-lax-lhr-dxb routing was preferable to the direct flight to dubai.
If the choice was in business class on that silly routing vs even economy on the direct flight on Emirates, I would pick economy every day, watch movies for 14 hours and land without any panics or sweaty runs to catch flights or risk of missed luggage etc
OP, your one and only problem was picking this routing when a very convenient direct flight existed. Time is more important than any anciliary perks of a better seat.