What I actually may be remembering is not a story that E'ch-Pi-El penned but one that he mention'd wanting to write. I quote from pages 894/895 of S. T. Joshi's I Am Providence:
"I'm not working on the actual text of any story just now, but am planning a novelette in the Arkham cycle--about what happened when somebody inherited a queer old house on the top of Frenchman's Hill & obeyed an irresistible urge to dig in a certain queer, abandoned graveyard on Hangman's Hill at the other edge of the town"
I love writing about antient graveyards, especially antient Lovecraftian graveyards. And I love seeing them depicted in art. I was so stunned with the cover painting for my book, Some Unknown Gulf of Night, because it evokes, so simply & beautifully, what I love about such a scene, the gnarled old trees, the moonlit slabs, the ghouls and freaks that frequent such a dwelling. I hope that I can actually overcome this current block and write my wee tale.