I knew I'd be getting over my head...here is the correct rule from bestof2k9 (An AE agent)

It applies only to SQ, for these two routings:

JFK-SIN
IAH-SIN

Here are the rules :

also note when O/B FLT is on SQ via the Atlantic, the I/B FLT must also be over the Atlantic.
- you can make a stopover in the city in which the SQ flight stops in, provided the routing is not over the MPM and only SQ flights are used.

Current routes: JFK-SIN (SQ via AT)
IAH-SIN (SQ via AT cnx city is DME)

So it's only applicable for ex-JFK/IAH and only to SIN. Not sure if stopover rules would still apply...in this case it would only be FRA if flying ex-JFK.

For the OP...looks like via the Pacific is most likely the only way to go...I'd go back to my first suggestion of OZ via ORD/ICN....if within the Permitted Mileage.