I was able to find a couple Saver awards in Singapore in first class via Singapore's website for dates that would work for me but then I was not able to see those flights on United's website. Based on what I have researched it looks like these flights are bookable using United points but that you have to call in order to do so and that they charge the phone fee even though the Singapore flights are not bookable online.

If I end up using Singapore Airlines, I would prefer to use United points if possible because I have quite a bit more United points than I do points transferable to KrisFlyer.