Have messaged the person saying that the listing will remain active and that I will be obligated to sell it to whoever hits the buy-it-now first.

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I think that makes sense. This person hasn't committed to buy, so you make no special concessions for them. Let them inspect and be prepared for the fact they may not buy there and then, might go home to bid.

It is not your concern if another buyer has bid in the meantime, that is a risk the potential buyer takes.

As someone else said, perhaps they will try to negotiate on price. That is where you just reply that you will be letting the auction run its course and the price is firm at the moment.