You could try this, too, especially if you have status. My husband and I recently had a 3 night stay at a Hilton property which we'd booked for a great rate about 6 months in advance. About a month in advance we realized we couldn't arrive for the first night, so I tried to rebook the reservation online, but the price for 2 nights was now about the same as the price for 3 nights had been earlier. My husband has Hilton Diamond status, so he called the Diamond desk. That agent said he wasn't authorized to re-price it, but he called the hotel on our behalf, and the hotel agreed to let us have the discounted rate, so the agent was able to drop the first night for us.

BUT after writing that, I re-read the thread and see that you actually want to stay the 3rd night but have it priced as a cheaper one-night stay. I don't think they'll price your other 2-night stay in your favor if that's the case.