I think this might have to do with TCP windowing, but not sure. I have been looking at using WAN Killer myself to do some MPLS testing and was told to use UDP and not TCP because of this windowing. I don't know a lot about it and haven't read up on it yet. Maybe someone else will chime in with some clear information because I would like to know before I start doing my tests.
I'm having a similar issue like you. Fortunately I have multiple sites so I was able to determine that the problem only occur on any of my International sites (I'm in Australia). My suggestion for you is to carry out FTP transfer test on a good site and compare the results with the bad site. That way, you have something to go back to the carrier and complain to them. I have seen mismatch duplex settings inside carrier's network that cause slowness