NC
Your first statement : “He gives you a down payment and then you repossess it when he fails to pay the full amount after Pesach. ” was spot on.
I believe there is a typo in your second though “The concept of the goy saying “I’m keeping the chometz” is basically a fantasy dreamt up by people who don’t understand how it works.”
As you correctly point out i your first statement if the goy were to pay the full amount after PEsach he would get to keep the chometz.
The “fantasy dreamt up by people who don’t understand how it works. is the reverse “thinking of not buying the chometz back from the goy” which as you correctly point out is hogwash, as thee is no “buying back”