And [hbdstabilizer] first needs to convert that to HIVE.

This is sort of true. Since the stabilizer is active 24/7, there are often conversions that started 3.5 days ago which are completing and delivering HIVE in real time when needed. Not necessarily 100% of the time, but quite often.

The stabilizer is aggressive in converting HBD because this is effectively a riskless operation for the stabilizer. Any "bad" conversions are effectively a burn of HIVE which benefits all HIVE holders (although would reduce the DHF balance somewhat). As a result there are many conversions in progress almost all the time.