Finding Star awards is needle in the haystack stuff, especially with SQ in C and F. For some years now SQ has specifically excluded the first and business products on its A380s and 777-300ERs from ANY Star award availability, but some report that this has been loosening a little.
Yet you need to be prepared to find very little on SQ for those aircraft, but there are a few regional ones. You'll have more luck with TG and CA, of course.
I used the
KVS Availability Tool to redeem BMI miles on Star Alliance flights (combination of NZ and UA flights LHR-AKL return in C)
It isn't free, but given you are saving thousands in airfares, it is a small price to pay to hunt down award availability. The twist is that you need to join the ANA Mileage Club to enable you to search (you do it online and it's instant), and then you will find availability.