Like WBT said, you probably don't have a choice in Europe, you'll have to go through London or Helsinki to go between CPH and Rome.

It sounds like you want to minimise flying time, so you can try:

YVR-somewhere in NA-LHR/HEL-CPH-LHR/HEL-FCO-HKG-SYD, but I don't know what that's going to achieve by saving one segment in Europe, except to minimise flying time...