There are so many things wrong with this purported buyer's strategy that it's hard to know where to begin.
The first, most obvious issue here is that he's clearly worried that if he doesn't persuade you to take it off the market before end of the auction, it will probably sell for more than he is willing to pay. My usual response to such offers (regardless of whether bids have already been received, which would preclude adding a BIN option anyway) is to invite the interested party to just bid that amount, and wait to win it. He doesn't need your permission or cooperation to do that, either; he can just bid right now. He might even score it for less, if his offer does turn out to be the best one.
His strategy to bid the price up to his offer and then have the seller end the auction makes no sense, because that relies on having some other bidder to bid against; otherwise the price can't go up. He could do it via bid shielding, using another account to counterbid the price up, but if he's already famliar with that little scam, he's probably not someone you want to have as a buyer.
Finally, his theory about having you send him a jacked-up invoice with additional charges to meet his offer is, I suspect, another scam avenue for him, since all he needs to do as the "winner" of the auction is to whack the Pay Now button as soon as possible, before you have a chance to invoice something higher, and when he's paid, you're on the hook to ship the item, even if you didn't get the extra money you were promised.
I'd just thank him for his interest and invite him to bid like everyone else... or else ignore him and block; your choice.
