The mystery:

Where are the other dies? Could this have been a single-die machine?

The mystery continues:

Here are other dies, but why are they misaligned, yet not quite as misaligned as you might expect from a single-die machine?

The solution:

Vertical dies! As far as I know, this is the only perforator that had multiple dies oriented vertically.

As a side note, although this perforator is listed as being located in Montreal, PQ, I have cancels on this pattern from Toronto, ON; Winnipeg, MB; Calgary, AB; and Vancouver, BC. However, I have no reason to think that there were multiple perforators or that the perforator was moved.