Hi guys, this my first time on here, so please be gentle with me.

I live in a south-facing three-storey tenement flat in Scotland. The result is that the back garden gets very little sun for part of the year, and none at all for the rest of it. Most of the back was in what was meant to be grass, but was in fact mostly moss and weeds.
I have now lifted all the "turf", buried it, and dug the lawn site to a depth of about a foot. To my surprise, the soil actually seems quite good, very black and friable, and reaonably free draining. After the first foot though, is a pan of thick yellow clay mixed with large stones, so digging it out is vitually impossible.
Having prepared the site, my original plan was to turf it, but I'm now wondering if seeding it with a shade-tolerant grass variety would be more effective.

Advice/opinions are sought please on:

The advisability of digging sand into the top foot to improve drainage, given the layer of clay beneath.
Pros & cons of turfing v seeding in the above circumstances.
Suitable varieties/mixes oif seed.

Thanks,

Ian