My family was supposed to fly Delhi to Seattle (booked through Amex Travel) and I could not get hold of Emirates at all. Tried Canada, US, UAE numbers, Twitter DMs, text, website chat… nothing worked for 72 hours.
What finally worked was turning on WiFi calling on my iPhone and calling the Emirates India call center number directly. I called around 11pm PST and got through almost immediately.
At first they offered March 8 to 12 on the same route, but I said I wasn’t comfortable routing through the Middle East given everything going on and asked about other airlines. They were able to rebook my family on Air France for March 12.
This was about 30 minutes before the original flight was officially cancelled. No extra charges, and Emirates handled it directly even though I booked via Amex.
Sharing in case it helps someone else. I was extremely stressed and this was the only thing that worked.