I plan to take an engagement ring to my prospective fiancee, value about $2600 (US), in July 2011.

If you will bring it back to the US, you declare when you enter and the custom staff will check when you exit. Then you do not have to pay fee. If you exit the country without that ring, you will pay for it. If you declare and leave it in China, you have to pay 10 percent fee. Don't pack it beautiflly and just put it in your handbag, and don't declare, you may pass the custom safely without paying tax for resonable amount of private thing can enter without paying extra money.