Riiiggght. Quite a DUH moment for me here.

Bulk Insert Task doesn't work if the table has more or less columns than the file has.

To make it work, I had to delete column 39, then run the task, then re-add column 39, then do my update on column 39. And if I'd looked at more than that one task on the original package, I'd have seen the solution.

I hope this helps someone else out. Quite a learning experience for me, this was. <headthunk>