It's not a perfect match, but your description is reminiscent of Theodore Sturgeon's short story "Yesterday Was Monday", first published in Unknown Fantasy Fiction, June 1941, available at the Internet Archive. In Sturgeon's yarn, we mortals are actors in a cosmic play. Sturgeon's protagonist somehow gets to Wednesday a day early and sees the stagehands preparing the set:
Swarms of little men who might have been twins of the one he had spoken to were crowding around the cars, the sidewalks, the stores and buildings. All were working like mad with every tool unimaginable. Some were touching up the finish of the cars with fine wire brushes, laying on networks of microscopic cracks and scratches. Some, with ball peens and mallets, were denting fenders skillfully, bending bumpers in an artful crash pattern, spider-webbing safety-glass windshields. Others were aging top dressing with high-pressure, needlepoint sandblasters. Still others were pumping dust into upholstery, sandpapering the dashboard finish around light switches, throttles, chokes, to give a finger-worn appearance. Harry stood aside as a half dozen of the workers scampered down the street bearing a fender which they riveted to a 1930 coupé. It was freshly bloodstained.
Harry meets "Iridel, supervisor of the district of Futura", who explains:
Iridel threw up his long hands. "My, you actors are stupid. Now listen carefully. This is Act Wednesday, Scene 6:22. That means that everything you see around you here is being readied for 6:22 a. m. on Wednesday. Wednesday isn't a time, it's a place. The actors are moving along toward it now. I see you still don't get the idea. Let's see . . . ah. Look at that clock. What does it say?
Harry Wright looked at the big electric clock on the wall over the compressor. It was corrected hourly and highly accurate, and it said 6:22. Harry looked at it amazed. "Six tw— but my gosh, man, that's what time I left the house. I walked here, an' I been here ten minutes already!"
Iridel shook his head. "You've been here no time at all, because there is no time until the actors make their entrances."
Same general idea as the story you described. However, I don't see anything about a huge ship sailing the timeline, or people losing their keys on account of continuity errors.