I'm confused...
Are you going to use United miles or transfer?
United.com does not show SQ 77W space (or any SQ award space). You need singaporeair.com to do that. If you want to fly SQ from the USA in premium classes, you need to transfer to SQ.
Your United miles should be able to redeem on UA, BR, NH or TG. There is a penalty of additional miles for non-UA redemptions, though.