I wonder if you could use leaves instead of hay? I know they would tend to mat down more- unless they blew away first. I have maple and mulberry leaves which I put in a pile covered with soil, small brances, and vines I've trimmed every fall.
Peasant (1963-1972) and Fluffy (1970s?-1982- I think of you as 'Ambrose' now)- Your spirits outshone some humans I have known. Be happy forever.