This is incorrect. SQ doesn't (at present) issue First or Business tickets to any Star Alliance carrier on the A380 and the 77W. However, they do issue F/J tickets (including to DC members) on the B747, 772 and 773 which fly, for example SIN-FRA/AMS, etc.

You might also consider flying on OZ in J LHR-ICN (Seoul)-SYD. This tends to have quite good availability.