After troubleshooting this for many hours (and trying all the suggestions posted here), the issue turned out to be the TLS link between our main office and the datacenter. I called our TLS provider and after talking to several NOC technicians, one of them had heard of the exact issue before. It turned out that some of their layer 2 equipment was old and had issues with VHD data.
The solution was upgrading the firmware on these devices, which was performed by the TLS provider. We now have no issues transferring large VHDs. For those interested, our TLS provider is Shaw Communications in Victoria, Canada.