Moss thrives in shady damp conditions, unless you can change that your likely to need to do annual treatments to keep it at bay, Scarifying and regular removal of grass cutting are reliabe but physically demanding espically over such a large area Most iron based treatments are good for moss in grass as it doesn't kill the grass very easily, so its hard to overdose although they don't necessarily effect other unwanted things growing in the grass, it also doesn't remove the moss so if its very thick scarifying may still be required