Even though DL publishes a D-I 30-minute MCT, it nonetheless requires all pax to be at the departure gate or face possible cancellation of their ticket. This is especially true if a flight faces an actual oversell. Given the conflict between MCT and DL's gate requirement, I would call DL and ask to be rerouted based on the published guidance.

As always, have the alternatives you want in hand so that you make it easy.

When traveling to/from a destination outside the United States, you must be checked in at least 60 minutes before your scheduled departure time and it is required that you be at the gate and ready to board at least 45 minutes before your scheduled departure time.
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Customers who fail to complete the check-in procedures by these deadlines will not be able to travel on desired flights and change fees may apply.