Actually, there are 3 different data sources for SQ Award Availability within the KVS Tool, 2 of which fully support Award Availability on SQ 388/77W/345 aircraft.
As
Savage25 says, none of which accurately reflect the extra availability you can book through BD. However, KVS and the like are still useful - if they say yes, then you should be good to go. If KVS says no, try phoning the ICC - there's a reasonable chance that Pune will be able to find you something.