Saw this thread at the top of the list and, though I'm not a US FF member, thought I'd pop in.

I've booked award travel using DL SkyMiles on SQ 001 SFO-(HKG)-SIN, most often returning on SQ 002 in the opposite directon, around the Christmas-New Year's holidays for five years: 2003, 2005, 2006, 2007, 2008. For '03, I booked in Business Class in March. For 2005 onward, I've booked in First Class, each year in January and February for the following December-January. Booking that far in advance allowed me to get pretty much the exact flights and dates I wanted. Booking a month out is practically out of the question. For this year, your best hope is to get a last-minute booking of unsold seats, literally a day or two in advance of departure when SQ releases additional inventory. This year, I happen to know a number of other DL SkyMiles members who booked award seats in First Class on SQ 001/002 around the same time I did ten months ago-- one even took the seat I wanted on SQ 002 for my return. We're all happy that SQ doesn't blackout the Christmas-New Year's period, but the award seats get snapped up way way way in advance.

Frankly, I'm surprised that the OP could get Business awards on LH connecting to SQ to SIN on such such notice. As for wrong way around the world: pish posh. It's about 22-24 hours flying time via FRA, versus 16-18 via HKG. I'm sure it will be a nice ride the whole way, and the extra time to sleep might be a good thing. I've gone to SE Asia from ATL via Europe once but usually over the Pacific. I enjoy it in either direction.