I would agree that relisting the item yourself on eBay is the best way to accomplish the sale, and perfectly ethical, at that. Many people do precisely that; I see this with some of the books I buy.
I am not so sure about the first option (offering the item to the second-highest bidder) would be looked upon kindly by eBay. They may take the position that you would not have had access to that second-place bidder, except through seeing his name listed in the auction bid history. This is even more true when you consider that, in most cases, you would need to use the eBay e-mail system to contact the bidder. Consequently, they may see you using the auction and eBay e-mail systems for purposes other than which they were intended. Better to have your own auction.