New lawn

I need to build a new lawn on a pile of clay. Area is about 100m square and very undulating. No vehicle access, no wheelbarrow access.

I have chucked a bag of gypsum on, I know I will need to rake it to try and level the metre high drifts. It's such a big job, where do I start and what do I do first, second, third etc? This is my back lawn - was flat and lush but had to dig a 20m drain from under the house due to seepage and I'm left with nothing but clean fill/clay.
I have access to a rotary hoe, how much of a layer of chicken coop crap will I need to dig in before I can sow lawn? Drainage isn't good due to clay but I can't dig more trenches.

You don't need chicken poo at all. But if you want to, you'd need to dig it in well.
Kikuyu grows in anything, and will hold together well, wet or dry.

You mention that you ‘need’ to build a new lawn on a patch of soil which by the sound of things is not really suited for growing grass, ( by the way kikuyu is not an option outside of warmer areas of New Zealand) , have you thought of planting a garden with plants more suited to the setting ?. If you need a flat area for entertainment/ play then maybe use pavers or a low raised wooden platform with a planting scheme that blends in with the house and surrounds .

I hate mowing lawns, so I had nine cubic metres of scoria dumped on my front yard. Since then I have dumped one cubic metre of fine limestone on top. That looks nice. The birds drop seeds, so I kill the weeds occasionally.