[The Squatter of Amon Rûdh]

Didn't Tolkien write a poem about the Anglo-Saxon's? I'm not sure, maybe that's just something else that I have it mixed up with.

You're thinking of The Homecoming of Beorhtnoth, Beorhthelm's Son, which appears in Tree and Leaf.

I have yet to read Gawain, although I've bought a copy and cheated by reading Tolkien's essay about it. Not surprisingly, the co-editor of one of the translator's sources is one J.R.R. Tolkien.