In the absence of other answers, I think your story, as described, has two features suggestive (albeit only approximately) of Frederik Pohl's "The Tunnel under the World" (copyright 1954, published in Galaxy Science Fiction, reprinted in "More Penguin Science Fiction", editor Brian Aldiss, Penguin Books 1963.)
In Tunnel, Guy Burckhardt wakes up on June 15th - every morning. So, not time travel, but time stasis, like "Groundhog Day". Also, he has a boat in his cellar. He finds the boat unfinished, even though he remembers finishing it. He does not, I admit, try to repair it by taking a part from the past. But I know how my memory conflates details in stories, so perhaps yours does. Do you think it might have been this story?