you will need lot more than 100K miles for SG return flight. you need 80K for US round trip on SIA for economy. too lazy to find out how much you need. Just check krisflyer.
unless your schedule is mad flexible, you aren't gonna find much. It's biz/first class for a reason; in general you are not gonna get crazy deals.
if you are smart you do what I do and have an airline reward credit card and build up hundreds of thousands of miles for free and can fly anywhere in the world first class for about $25 in fees total.
The cheapest fare you will get for 1st class tickets is to upgrade when you check in at the airport. I flew from Los Angeles to Japan and it cost me about $600 to upgrade.
Another option is if you know someone who works for an airline use a buddy pass. No guarantee you will get 1st or Business class since you are standby, but for an international flight it has worked for me about 75% of the time.