Dan:
Your chrome dome is very nice. But when you say there's no serial number - I'm assuming the rating plate is there but the riveted-on serial number is missing? In 1964, Rainbow brought out the 'new' plastic dolly and the jet air rug tool. The old style rug tool pushed quite hard because of the air seal to the carpet. Since your chrome dome has the new style dolly, rug tool, as well as 'ring type' suction control, your machine would definitely not have had the 'odd' rug tool originally. Is it possible they had a gold model D or an early Chrome Dome (with that nozzle) then traded it in on the newer model but kept the old rug tool?