This is what it says on the website of China's embassy in Washington:

Citizens holding ordinary passports issued by the following nations is exempted from applying for a visa if he or she joins international tourist group organized by any of the registered travel agencies in Hainan Province which is approved by China National Tourism Administration and stay up to 15 days: Australia, Austria, Canada, France, Germany, Indonesia, Italy, Malaysia, Netherlands, New Zealand, Philippines, Russia, South Korea, Spain, Sweden, Switzerland, Thailand, U.K, U.S.

I have not found any article clearing stating US citizens (unlike those from Russia, North Korea or Germany) can visit Hainan in group of 2 without joining a tour or having a visa.

I'd be shocked if CX or KA will let you board, and if you do, I'd be shocked if the Chinese didn't send you right back and fine the airline.