There is some good use of 2-4-1s in that itinerary. I also think LHR-SIN in F is a good choice; long flight on the A380, I assume?

On the internal AA flights, you may find it worth paying for AA "First" - sometimes it can be a surprisingly small amount extra, for a much bigger and more comfortable seat on a longer flight such as LAS to DCA.

On all the AA flights, make sure you select seats using your BA Silver status, and if "Main Cabin Extra" or exit row is available, take it.