The red clay is probably the reason the "Old Lawn" failed... what is going to be different with the new lawn??? the first thing that needs to happen is that something is done to make the red clay more user friendly... levelling with a heavy machine isn't one of them...
I would till in a sandy compost to the depth of 8" if possible... then I'd leave a layer of the sandy compost after I raked it level to desired grade,,, by hand,,, with an iron rake...
Should you really irrigate the red clay twice a day??? I'd check the conditions of the place where its laid for 2 or 3 days just to make sure destroying the buffer zone where the roots are supposed to grow...
How a given soil handles water is your primary concern, especially with clay...
