Well, I have apparently resolved this problem by moving the Sent Items folder contents to another folder and running a restore on both folders. The relentless growth in bandwidth has stopped.
I was guided to the source of the problem when I tried to open the Sent Items folder from the SM web interface and got a time out.
I have no idea what was happening but I suspect that SM was somehow fooled into thinking that the contents of the folder were being continuously sent when this was not the case.