Joseph, from what I’ve heard of the halachos, it might not be so simple (as others such as DY have pointed out here). You are raising a good point, but I think the halachos are more complicated than that, and you should look into them.
And anyhow, the sale is done through the Rav, so you couldn’t have made a direct deal with the goy after Pesach. Do you even know who he is?
I actually met him once. I got to the Rav’s house to do mechiras chometz so last-minute that the goy was already there!