If you put the irrigation system first, you are likely to tear up some
pipes and sprinkler heads and bodies when tilling and at best, have to hand
till around the sprinklers which is a real pain. Especially when it's hot!
Kill it first. Give it about a week to make sure the Roundup or whatever you use is working well. Apply more roundup to kill any stragglers.
After its all dead, mow it as low as possible and rake it clean, then till it. After tilled, go ahead and do a rough smooth out and remove all other dead grass and weeds with a rake and make sure you don't have any large clods of soil, then put in the irrigation system.
After the system is in, final smooth it out and hydroseed.
good luck
dd
experience is something learned, just after you needed it most