Some further thoughts:

1) Generally SQ do not make space available to star alliance partners for upgrades/business class redemptions on their long haul product (A380, 77W). I understand an exception to this is Miles & More and airlines that seem to be aligned with them
2) I have heard that Avianca Life Miles program has the same access as Miles & More (not sure if this is true or not)
3) If it is true, I know that Life Miles doesn't see any availability on SW Pacific (Australia/NZ) routes until 14 days before departure.

One suggestion - sign up for a free Life Miles account and use that to check availability of business class redemptions, and if they come up then get straight on the phone to Miles & More.