Maybe just a gov't brown envelope with 34 twenty's?  

Who is going to cash the cheques other than a money mart sort of establishment, or has a chartered bank stepped up to provide a banking service?  The cheque recipients have no fixed address and probably minimal documents to support their identity.  With a little ingenuity, this could become rather problematic and I would not be terribly surprised if more cheques are issued than irregular border crossers accounted for.