I flew SQ for the first time in July: LAX-TPE-SIN-PEN. Even though I needed three segments to get to my destination, I enjoyed every minute of it.

Here's another possible option for you. SQ now has business-class only non-stop flights from LAX-SIN. I know that you are in SFO. But since you'd likely have to connect from SFO to another city to get to SIN anyway, exploring the LAX-SIN route is a consideration.

Availability? Well, that's another story. I'm not certain that SQ offers award travel on the LAX-SIN route. You should pose that question on the SQ forum.

Also, no matter how you get to SIN, you are looking for award travel perilously close to your travel date. So that could explain your difficulty in finding a routing.