Throttle copying our data

GoodDay community ,

We are supposed to switch over so that our users end up using OneDrive as their home drives and Copy a lot of large files to Azure Blob. We thought we had everything ready to copy during our testing but our network got so saturated due to the bandwidth consumed.  We opened a ticket with MS premier support and our assigned PFE engineer to see how we could throttle Azure Blob and throttle down the copying speed to OneDrive. Microsoft said there was not a way to throttle and our google searches came out with nothing. 

 We are looking for some software that is "reliable" but can throttle copying data to OneDrive and Azure blob. (Azure blob to give you an idea is sucking 80% of our internet connection (just one server). While budget can be an issue, we do not care at this point as long as we can get something reliable. We do not want something that does blackout hours as our operation cannot be interrupted at night.

 I am hoping we are not the first ones to run into this situation .

Notice : my question posted on the other communities , and I still have no dependable answer ! Thanks