I visited DUbai back in Nov of 09, I flew the eastbound portion of the journey nonstop out of SFO on EK nonstop (flight was wide open). On the return I flew on KLM via AMS and connected on to SEA on DL. The KLM flight was wide open so our seats were released at the ticket counter about 3 hours to departure.
That being said May is not high season in Dubai so you should not have a problem going through Europe (the nonstops to the US ar ea bit trickier)
Keep in mind- UAL flights to IAD usually go out weight restricted. DL's flight to ATL is quite popular with non-revs and usually has high load factors.

Regards,

Chepos