There are other ways to save your internal bandwidth from starvation due to a QoS applied on the internal interface.
First of all you can remove the QoS on the internal interface and limit the application on the external interface. Maybe you will have to limit the ACKs and not the actual packets of the specific flow, but it will do.
Secondly you may reserve some bandwidth for management purposes.
If you don’t want to remove the QoS from the internal interface, at least raise the bandwidth of the inside interface and add a class for the management traffic.