It takes round about 12 Constructors if i counted correctly, + some for Base Defence and stuff
End of quote
Actually that's a lot more than you need. If you keep out of wars (just keep the AI fighting each other and not you, more trade money that way too!) you don't need defense modules, and the earlier culture modules aren't really worthwhile unless you need every last bit.
All you really need is 6 constructors to build straight to a palace, then squeeze as many starbases into a sector (9 I believe is the most you can get now with the 3 parsec rule?) adjacent to one with enemy planets.
Note that there are some mods that add more big culture modules after palaces, which make this even easier to accomplish.