Sorry, I edited my comment so now your response seems misaligned. I changed my comment to reflect that the originating flight from DXB doesn't line up with non-stop to SFO well.
Are you sure?
aa.com will sell me
01:55-06:20 AA6416
11:30-14:20 AA6188
Do you have lounge access ? if so surely that might be your best bet ? and would avoid an extra connection in the US ?
Both of these are operated by BA and on 744s
cs