At least to YVR, you'd end up back in NA via JFK. Then take the JFK-YVR flight. This forces an overnight in NYC (since the direct flights are all in the early am) but is otherwise doable.

My main concern is what type of available does SQ give its own RTW fares. If it is ultra-tight, then it is useless. Given all of the restrictions SQ puts on fares due to their new business and suites, it could make an RTW almost pointless.