Actually I had not intended to mulch the asparagus with fabric but it was the quickest way to deal with vigorous buttercups pushing through manure. Everything has happened so fast here and I would have done better to have mulched the ground for a few months before planting. So it is experimental and I plan to remove the fabric by midsummer, may have some perennial weeds to trowel out. I have not cut any holes yet as there will be no spears pushing up until the frosts have finished (four weeks?).
Your plot sounds well prepared at least! Asparagus grows stronger on rich soil but if your underlying soil is in good heart, the green waste compost on top will be fine for now, with plants so small.