Also search for RTW fares....as thats what you seem to be possibly doing...
Recommend giving matrix.itasoftware.com a look...
Using 8 to 22 March a simple return SIN-JFK (fr'instance) is as low as $798 on CZ (China Southern)
SIN-JFK (stop)-LHR(stop)-SIN around the same time as low as $1500 (but goes via LHR on the way to JFK so you might do better going to LHR first???)
Have fun...good luck,
LOL....just realised LHR first was likely the plan....