If you either have Skype (or something similar) or don't care what it costs, start dialing US in other countries, preferably places where it is during regular business hours. Expect the call to be answered in the language of the country you are calling, but also expect the agent to shift to or shift you to an English-speaking agent if you start out by slowly saying, "I only speak English".

However, if all you want is a refund because your flight has been cancelled or you have been auto rebooked onto an unacceptable routing, the COC entitle you to a refund. Thus, no need to torture yourself. Let it go and deal with it after the fact when the lines are clear or you have to be at a US ticket counter anyway. Needless to say, your refund will be delayed at least by the time you delay, but it is well worth it. If you really want to protect yourself, send a webform complaint to US noting that you attempted to call before the scheduled departure time, but could not get through and would like a refund. It won't do much but make you feel less stressed.