Omg thank you for this thorough explanation. I’ve read many, but none covered it this well.
Odysseus let the swap happen to protect Antinous’s father from the public shame of his son being a coward. Antinous got selected in the lottery, freaked out, and basically bought Sinon’s place with a promise of money that never got paid. Odysseus covered it up so the noble family wouldn’t be disgraced. That’s why Sinon ended up at Troy instead.