The first town, Ur, should be the settler factory. It needs a granary and +5 fpt, which you will get from working the cow and no 1f tiles. The following sequence should work just fine:
3.5->4.0: (City Center), Cow, Silks, mined BG, forest on growth => 7 (7)
4.0->4.5: (CC), Cow, Silks, 2x mined BG => 7 (14)
4.5->5.0: (CC), Cow, Silks, 2x mined BG, forest on growth => 9 (23)
5.0->5.5: (CC), Cow, Silks, 2x mined BG, lake => 7 (30)
Takes a little bit of micromanaging, making sure that the citizens are assigned to the right tiles each turn, but I assume you do that anyway.
So, what you need to fix is two mined BGs for your capitol, and a granary.
Sumer should be a military town. Build a barracks, connect your iron, and start pumping out swords. To get up to 10 spt (actually 11 because of corruption) you want to mine its three BGs. That together with a forest and the iron and the city center should give you the necessary 11 spt at size 5.
Btw, skip Warrior Code, you can have it from me. Go for The Wheel instead (again). Not because we need the horses, but because we want to know where their sources are.