One of the most satisfying things about collecting prewar cards, at least for me, is researching the players and the cards themselves. Today, after poring over several weeks of scanned archived editions of the Altoona Tribune, I am happy to say that I found the ad that first announced the availability of these cards, on June 12, 1916:
There had been a short blurb of only a few lines in the June 9 edition telling readers to be ready for a special announcement that next Monday, so it seems this ad had not appeared before and the cards were thus available on the 12th for the first time.
The following day the paper heralded that these cards were a rousing success:

Interestingly, both the ad and the account mistakenly stated that among the cards the kids would/did receive was Matty, who was not in the set. Anyway, another part of the puzzle solved.