As number_6 states, you have mutual exclusive requirements. The least objectionable route would be to do HEL-xxx-LHR-YYZ/YVR... and choose a city in Europe that arrives at terminal T4. That is the terminal where the trans-atlantic flights on BA depart.

Wait until 1-Apr and go via BUD and for a really round about route, fly via AMM as RJ has service to YYZ from Jordan. The middle east is part of Europe for the OW explorer fare rules. And that is not back tracking either.