I finally bought the ticket, but it was much more difficult than it needed to be. I'll describe this in case anyone is looking for this information in the future. This payment situation must be specific to fights departing China.

I didn't want to use an OTA since all of them, including Ctrip, were showing a higher fare.
As mentioned above, if I choose KRW, the only options available were card issued in Korea which required selecting from a list of Korean banks or UATP. When selecting CNY, the only payment options were Union Pay, Alipay, and Wechat; with no option for credit cards. This contradicts the payment information section of the website which indicates CC are accepted for China

Since the US reservation office was closed, I called the Korean office. They told me they are unable to take cards issued outside of Korea, and suggested I call the China office. I called the China office, and the agent seemed surprised when she checked and the option for a credit card was unavailable. She put me on hold for a while to check with someone. She came back and told me that that function was previously there and she didn't know when or why it had been removed. She said that it might appear again in a few days but didn't know.

Rather than wait for the US office to open, I decided to use Alipay (forfeiting 5X Amex MR ��) . I was able to create the reservation on my computer, and then process the payment on my phone using the bar code from the reservation. But this being China, just as the transaction was completed on my phone, my internet connection dropped. The website was showing that payment had failed and no ticket had been issued, even though I received a confirmation from Alipay. I called the China office again. The previous agent I talked to had great English skills, but this agent and I had great difficulty communicating with each other. Just spelling my name and giving flight information was a task. She finally told me that she would submit a request for the payment to be checked and I should get a confirmation within 3 hours.

Thankfully, I received the e-ticket in my email about 20 minutes later.