It turns out Davidman is retelling, probably from memory, a story that had been published in ASTOUNDING back in March 1940: "THE DWINDLING SPHERE" by one Wm. Hawkins. I've never heard of Hawkins before, but a subsequent posting provided a link to the entire story online:
Interestingly enough, this story seems not to have been reprinted or anthologized between its original publication and the date of Davidman's book.* Also, it's clear from reading the story itself that it differs a good deal from Davidman's version, which is thus probably being retold from memory (which might explain why she fails to name the author) or only known to her at second-hand, in a version told her by someone who remembered the gist of the story but not any detail. The most significant departure is that Davidman provides an ending for the story (a brief glimpse of the last human, floating dead in space, after the world has been completely used up by its inhabitants): an ending entirely appropriate and indeed rather better than the one the original author provided, but definitely not taken from the 1940 publications.
And this offers up some interesting possibilities. Did Davidman read this story when it first came out, when she was in her mid-twenties? If so, that wd suggest she was more deeply involved in science fiction than is our general impression of her. Or was the story told to her at a later date, which wd suggest she was plugged in to the science fiction community (fans and writers) more than published accounts have let on. Now that we know her husband knew Heinlein, and Fletcher Pratt, et al, and that Davidman knew Clarke and John Christopher, maybe it's time for someone to research and write up a piece on "Joy Davidman and Science Fiction".
current reading: INTO THE WILD by Krakauer (just finished), FRANZY AND ZOOEY by Salinger (still painfully slogging through), TOLKIEN'S BEOWULF (re-started)
*rpt in MASTER'S CHOICE, ed. Laurence M. Janifer ; THE GREAT SF STORIES 2 (1940), ed Asimov & Greenberg (DAW, 1979); ISAAC ASIMOV PRESENTS THE GOLDEN YEARS OF SCIENCE FICTION, ed Asimov & Grrenberg (1983).