hey cardigon,
unfortunately you can't cut the DIN cable and twist on a BNC connector as each of these connectors have different cable requirements. here's an item that was recommended to me and this or something similar might suit your needs:
http://www.bhphotovideo.com/bnh/controller/home?O=productlist&sku=589906&Q=&is=REG&A=details
having only BNC connectors on the back of your monitor this type of adapter would provide power to the camera.
being that the above item is a Lorex brand adapter it may have (most likey has) a proprietary pinout on the female mini DIN connector and may not match up to non-Lorex cameras with the same 6 pin connector type. you might check with the camera's manufacturer for a similar item.
cheers
cheers,
tom