Just remember that Windows isn't the only thing that restricts your power.  There are BIOS settings to consider, and, if you're running virtual machines, there are possible throttles there too.

Best way I've found of speeding up AzCopy is by tuning the number of threads used - parameter "/NC" - have a look at the documentation https://docs.microsoft.com/en-us/azure/storage/common/storage-use-azcopy#azcopy-parameters

Suggest you start with this: https://www.red-gate.com/library/sql-server-transaction-log-management

Depending on the data, you might get some benefit from using a WAN compression device, but they're not cheap.  And I guess you haven't got one of those to hand,...