If you are using the [Awards/AC-StarAlliance] Method in the KVS Tool, there should be no need to call ICC.
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.
Blocked SQ 388/77W/345 seats are shown using a special indicator (~), as a further reminder to select a different Method.
BD has far more premium SQ availability than any of the many online tools. You have to call to find out though.