Not knowing more about your timing constraints or your level of flexibility etc. it's tough to make sweeping changes, but herewith a couple of questions...

1. Has this itinerary been approved by BA or whoever would be issuing the ticket, or are you using the online tool? Your YVR-NRT-SYD-SIN is questionable even assuming the NRT stop is just for a connection. Most airlines have interpreted the "second Asia entry" rule as being limited only to transits between Europe and Australia/NZ, not N. America and the SWP. It seems like the online tool doesn't recognize this glitch, but I would still be nervous about it myself. If the NRT stop is actually a stopover, then the route is invalid.

(As a personal note, I found JL's NRT YVR service to be less than stellar, YMMV.)

2. Have you considered starting the trip somewhere else and using LHR only as a connection point? With current currency rates, the price will be very close; it might even be a few quid cheaper to start in, say, AMS or CDG (or possibly quite a bit cheaper to start in one of the current "cheap" European countries like BUD, WAW or ARN.) Plus, by connecting through LHR on the way to N. America you'd avoid UK APD on the departure, which is not inconsequential. Obviously you'd have to pay to get to and from the origin point, but this often can result in net savings anyway.

3. Obviously you're leaving several N. America segments on the table; the TP harvest from which could be quite high. You could solve the problem in my first point by reversing your route, e.g. LHR-YVR-JFK-SYD, or even LHR-YVR-JFK-ORD-LAX-SYD for more tier points and a chance to ride the QF A380 over the Pacific.

There are many other route modifications that could yield many more miles and tier points, but that would depend on your flexibility.