In general this should work. What you could do:
- Instead of going back to LHR go to ia different place in Europe. If you travel C you will find tickets in the UK more expensive than other places (like CAI etc.)
- You could also buy a Europe-NY-SFO with stops in NY, which would give you the additional transcon
- Not sure about Australia. Is the limit one transcon or one flight to NZ? (SYD-PER-MEL)
- Check if RTWs are cheaper from Europe (non UK). You could start there or in Canada.
- Also check, not sure if it is possible to travel the same sector twice (JFK-SFO)