Years ago I did a similar routing before I was even a FT lurker.
I did JFK-(FRA)-SIN-PVG-SIN-(FRA)-JFK
I didn't even know that the plane was stopping in FRA until I got on...I thought it was going the other way around the world. It's valid since you're not actually executing a stopover in FRA. There is a small chance that an uninformed agent might try to charge you more for stopping in Europe. If that happens, follow FT Rule #1, politely say good bye and call back.
Now, the real trick may be availability, and yes, this is a painful, painful route. Changi is the most beautiful airport I've ever seen though.