Hank, there are 18 confirmed advertising backs--the three known companies with full sheets did not have advertising on the card backs. They presumably ordered these sheets and were not provided them gratis.
Yes there are varying degrees of scarcity among the card backs. Sporting News is most plentiful, as it appears to have acquired licensing rights a few months into production. I would not necessarily agree that the promotion was a bust, as 18 advertisers in 13 or 14 states shows that it reached throughout the country. The fact that Mendelsohn offered the complete set in sheet or card form to the general public probably didn't help his advertisers much.
10,000 cards as a minimum order seems about right to me. Keep in mind that just because few sets survived doesn't mean they were not out there once. For example, Morehouse Baking in Lawrence Mass, which is of medium scarcity among m101 backs, offered prizes for redemption of the complete set, and several examples of Morehouse cards bear a redemption stamp, indicating that the prize was issued and the cards returned. So some sets were indeed amassed, yet the odds are very long against completing such a set today.
Yes it was presumed (by me anyway) that the card backs were produced by Mendelsohn or his subcontractor(s), as it would seem unwieldy to take them in already cut form and then have them individually printed on the back. I suppose complete blank-backed sheets could have been ordered and then printed (not stamped) but that would have been a hassle I assume most advertisers would have wanted to avoid.
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If we are to have another contest in the near future of our national existence, I predict that the dividing line will not be Mason and Dixon's but between patriotism and intelligence on the one side, and superstition, ambition and ignorance on the other. - Ulysses S. Grant, military commander, 18th US President.
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