The Downs poster was featured in the "Nielsen Gallery" (a monthly write up of a classic poster from the Norm and Lupe Nielsen collection) in M-U-M last September. It was listed as "Circa 1903". It was printed by Carqueville Litho in Chicago and is their Litho #2369 which would help date it more precisely if one had access to the company records. The company still exists and has a website, but did not respond to inquiries regarding the poster when the article was in preparation (the Nielsens rated the poster as "scarce" rather than "rare", meaning that they know of at least 12 copies of the poster, though they note that most are not in good condition).
I am pretty sure the T. Nelson Downs window card that reproduced the poster in black and white was to promote his appearance at the third IBM convention, in Lima, Ohio in 1928 (similar window cards for Axel Hellstrom, Cardini, and probably others appearing at the convention were also produced for this event).