Sorry, solving the issue you're dealing with is a bit more involved.
Whenever you have a multiple node (some kind of mesh) topology, you often encounter the problem that the sum of multiple nodes sending to one node can overrun the receiving node's bandwidth. The general QoS "fix" is a QoS policy on the service provider's egress link to each node. MPLS vendors often support this, some charge extra to provide it. Such a QoS policy does not preclude the common need also for a QoS policy on your equipment's egress link to the service provider's network.
If the foregoing isn't possible, then what can guarantee bandwidth management would be every node having a policy that limits the bandwidth that can be sent to every other mode, and the bandwidth allocations of all the nodes allocations don't exceed the available bandwidth to each specific node. For example, if you have a four node network, and one of those nodes had 2 Mbps of traffic, the aggregate of the three other nodes' policies should not exceed 2 Mbps to that 2 Mbps node. As might be imagined, this doesn't scale very well, and you often have much unused bandwidth.
Another "solution" is to rate limit traffic on ingress from the provider. For example, traffic like your heavy file copy, in your OP, would limited to 50% of the ingress bandwidth. Besides, again, you'll find bandwidth often going unused, upstream bandwidth hogs will often (repeatedly) burst a link to capacity before slowing because of detected drops (due to the rate limiter). I.e. this "solution", really isn't one.
Yet another "solution" involves using a traffic bandwidth management appliance (I'm unaware of any in Cisco's product lines, but there are some 3rd party devices for this). Such devices will manipulate what the sender's "sees" as the size of a receiver's RWIN and/or delay sending TCP ACKs. This "solution" will generally work better than an ingress rate limiter, but such traffic appliances aren't always 100% good for reasons I won't go into. (Although, it should be noted, they do confer some other advantages, which I also won't go into.)
