I was able to book an international Aeromexico award a few days ago with no issue. The wait time for an agent was incredibly long though. I checked and I called the same number you have in your reply.

Before calling I found award availability on the Delta website and double-checked on FlyingBlue.

When I spoke to the agent, I stated that I wanted to book a partner award flight on Aeromexico. They took down the passenger information, created a reservation, and requested availability. It came back confirmed and I had no issues booking it. Not counting the hold time, I had the flight booked in less than 10 minutes of speaking to the agent. I did not have to do anything special on my part.