You might try visiting the KH with an American flag pin in your lapel. In 2003 I visited a KH during the Memorial. I dressed conservatively, suit and tie, but I also wore an American Flag lapel pin. The JWs were very friendly, finding me a seat, loaning me a songbook, even telling me of their free home bible study program. They treated me like royalty. I've done this at other KHs with the same result. You would be surprised at the JW reaction to "Old Glory."
Outside the USA you should use the flag pin of the country where the KH is located.