I think the possibility of a chain store agreeing to refund and rebill is essentially zero unless you physically return the merchandise and buy it again.
Typically when there is a sale within a certain time of purchase, most stores if not all do an adjustment by just showing the receipt, be it on the same card the purchase was made with; It has been my experience. But do not know if it works with 2 different cards even with the same issuer.
All comments are appreciated nonetheless.