Office 365 Traffic Shaper for migration

We are moving the entire company to 365 in the next couple of weeks. Tentative cutover date of 12.20 or so.

Unfortunately, we have a few sites with some substantial bandwidth limitations.

Any tips on creating a traffic shaper or other method for allowing 365 to use all available bandwidth, but subordinating that bandwidth to everything else? The whole system is gonna be bogged down for a couple of days if everyone is downloading 10GB email boxes.

From what I can tell, I think I need a shared reverse shaper, correct?  But I don't really want to CAP the bandwidth.  If nothing or nobody is using bandwidth, 365 can have all of it.  But if someone needs a file from the data center, 365 needs to slow down and make room for that.   

I currently have a single outgoing policy for Office 365 so i can apply different security to it vs other traffic.

all locations are either 60Es or 80Es on 6.2.1.

Thanks.