If you can find availability (and it's a big IF), the part I've bolded is your best bet. (Finding F or probably even J availability on UA SYD-LAX is extremely hard, especially if you are not doing it 330 days in advance, and in any event it seems you don't have enough miles, plus the SQ F experience is much, much better even though it would be a shorter flight.) If you book online, you get a 15% discount on your SQ miles, so you'd seem to have enough for NRT-SIN on SQ's best plane, the A380, which has an enclosed suite for its F seat. It's 60K miles, less the 15% point discount, so your 57K total UR/MR would seem to do it. Here is the award chart:
https://www.singaporeair.com/pdf/pps...wardCharts.pdf
What you'd do is this:
1. Establish a Krisflyer account.
2. Once you do that, you can search online at Singapore Air to find award availability.
3. If you find availability, transfer you UR and MR points to SQ and hope the availability remains for the one to three days it will take for your points to be converted into KF miles.
I just did a quick check and found availability on Aug. 8. Didn't check too many other dates.
Now, for the same miles you should also be able to continue from SIN on to BKK in J, but that's a more complicated strategy since it involves a phone/skype call and trying to find an SQ customer service rep who knows the rules properly. Feel free to private message me if you want more of an explanation.
Hope it all works out!