I don't know if there has ever been a bulk-banking from WSJ - more like a week here and a week there. This is by far the hardest exchange in the Starwood system. Have you checked the Sightings Board?
Using the search function on the Sightings board, all I see are 3 separate weeks that have ever been reported in Sightings. Since Starwood controls the II deposits at this resort, and the MF's and purchase price are very high, I think it's rare for them to be deposited with II.
Since the Starwood priority also applies to on-going searches, your best bet is to place an on-going search for any available date. On-going searches are filled before anything shows up online, and that's another reason for so few sightings.