Seems strange that SQ is only being added to flights from/to JFK SQ codes will work for BOS-JFK-FRA-SIN but not BOS-SFO-HKG-SIN or BOS-LAX-NRT-SIN (same for FLL) which seems odd to me.
Not really odd, codeshares work differently than alliances/ATI agreements. It's not unusual for airlines to only want the codeshare out of a major hub where both airlines operate (in B6 and SQ's case, JFK, since SFO and LAX are spokes).