[EC2 Windows] Move MAC address across AZs

My (Windows) application relies on license keys linked to MAC addresses. Getting a license key assigned to a new MAC address is a hassle, I need to request the vendor to do this manually. I use ENI to retain the MAC address of the (on-demand) EC2 instance when it's stopped / terminated. Based on the documentation, I understand an ENI is linked to a specific subnet and hence cannot be moved across AZs. This limits my flexibility in moving instances across AZs, e.g. when encountering (last minute) capacity issues in a given AZ.

Is there any way to migrate the MAC address across AZs?