I like the sound of Heath cottage. I guess it is because Heath means a large area of grassy land in England, as in Hampstead Heath. I had completely forgotten that aspect until reading your post.
I would not mind betting that there are a few Heath cottages in Yorkshire, bearing in mind Wuthering heights and it's man character , Heathcliffe who our beloved Heath was named after.
The Bronte sisters all lived in Yorkshire and in fact you can visit their house. You I am sure would feel some empathy there, knowing the connection with our lovely Heath.Do not forget Bettys tea rooms ig you visit York and if you do, take a picture. Despite living in Cheshire, York town is one of my favourites.