Even more extreme on OW would be LHR-SIN-SYD-DFW-SFO - 4 flights but a heck of a lot of hours.

On a more serious note, if the OP is determined to add stops and connections to a simple, safe itinerary, there's presumably a routing via HEL and somewhere? Also I vaguely recall IB flies to LAX though that may be seasonal, and there are probably options via SJU though it's a long detour.