You can't break it and try upgrading individual segments on one award ticket.

I suggest you book two one-way awards: PHX-LHR-DXB and DXB-LHR-PHX. Once you get enough miles, you can try checking for availibility in F.

If you booked it all as one award ticket, you could only keep checking until the start of the first segment. With two one-way awards, you will have more time to try upgrade the return.

(I'm not suggesting four one-segment awards, as that will cost more miles to start with. But the two one-ways between PHX and DXB should be the same cost as a return trip between the two points.)