Planting in dry shade

The garden has an old and quite large damson tree which fruits and which is also enjoyed by the squirrels. But of course it creates shade. And because of the walls on two sides of the garden I am challenged by snails and slugs. I am starting to think what I can do with the space under the tree.

The tree is on the boundary, with a new fence behind, something like the fence below, and I am thinking about plants such as Liriope Muscari, Anenome Honorine Joubert, Bergenia Abendglut, and maybe moving towards shrubs such as Cornus Alba Elegantissima. What do you think?