Mossy lawn areas gone - despite creating more shade on it.

For the first few years in this garden we had loads of Moss in the lawn. then we planted a mini orchard in it. I let the hedge grow taller and it shaded the grass more, then we'd cut the grass and leaving clippings on top, and even just mow the fallen beach hedge leaves into a mulch in situ - all bad things apparently as Moss is meant to love this. We used to be able to rake moss up in abundance to add to pots etc.

The anti moss things we have done though may include sprinkling fire bowl ash around the garden and sprinkling used compost in the mossy areas, also letting the grass grow a bit taller between cuts.

Anyway, this last year i'd say the moss in the lawn is pretty much gone and the grass is lush - more by luck than judgement. Was this 'feeding' of the lawn part of the answer. Might anything help others in what we did?