EDU Tenant - File Migration for OneDrive for Business

There was the Office 365 Import Service but a few months back the service https://blogs.office.com/en-us/2015/09/16/office-365-import-service-migration-to-sharepoint-online-and-onedrive-for-business-just-became-easier/ importing data to SharePoint Online or OneDrive for Business, either by using the drive shipping or the network upload method.   This service now only seems to support PST imports (buried in Security & Compliance/Data Governance/Import by the way).  Shame Microsoft took a step back from this very common workload.

Microsoft now recommends this method, which I think would work with OneDrive as well - https://support.office.com/en-us/article/Upload-on-premises-content-to-SharePoint-Online-555049c6-15ef-45a6-9a1f-a1ef673b867c.  I don't think anyone would be in a hurry to use this way for significant migration work but I could be wrong.  Sharegate is a great tool and it is economical, compared to similar products in the marketplace. 

You may have done this already but I'd take a step back and look at that 4TB of data, has it be pared-down already with a data cleansing exercise, as that's a lot of data (pointing out the obvious!).