Warpus your garden is "flat".
From my shed I look down on the roof of my house.
I have a bench behind the shed that looks down on my shed roof.
Grass will grow on 45deg slopes in the medium term.
I would only grass the two sides away from the fence, and leave the side against the fence as is. It would be difficult to cut grass here and the stone will keep the weeds down.
As Cutlass notes above 125 to 150mm of topsoil that you have excavated will be good for your grass on top of the stone. It will grow on less but it will more likely die back in a drought.
I would come out level form the top of the slabs about 100mm them slope down to the existing lawn. So the topsoil will not be so thick against the slabs. I would make the length of the slope the same width as your lawn mower, it will make it easier to mow.
Place your topsoil and walk it down to compact it.
Leave it for a week.
Couple of days before you are going to plant your grass lightly rake the surface. I would not bother with the fertilizer.
Spread grass seed etc as BBC. I have never protected against birds.
When you water do not do to much at once as you do not want to wash the grass seeds down the slope or turn the topsoil to slurry.
Grass will come up in a few weeks.
Mow next Easter.
http://www.bbc.co.uk/gardening/basics/techniques/lawns_sowlawn1.shtml