That is an unusual Kenmore, and I can't say I have ever seen one in person.
The top and lid are the same as Hotpoint and JCPenney used for a few years when production was moved from Chicago to Louisville Appliance Park, before they also got the GE style lid with the clipped corners. The Viking (Eaton's) washer pictured in the "BOL GE and Hotpoint" thread also has this Hotpoint type lid.
Since the matching dryer is in Canada, and the washer in upstate NY, I question whether these were ever sold in the US. They may both be Canadian models. Sears Canada has continued to publish full catalogs unlike in the US, so maybe a look in the catalog from that time would give some clues. If they were sold here, I don't know how I missed them.