This force, while inspired by Henry Christ's 203rd Force from Annemann's S-h-h-h-! It's a Secret, 1934, p. 41, was, according to Ken Krenzel, the idea of Edmund Balducci. Krenzel knew Balducci well, and co-authored with him the first published trick to describe the force: “The All-fair Coincidence” in Hugard's Magic Monthly, Vol. 14 No. 6, Nov. 1956, p. 502.
Nevertheless, Karl Fulves, in Prolix, No. 4, Aug. 2008, p. 270, points out a close precursor in Sam Mayer's “Another Do as I Do”, in the Sphinx, Vol. 45 No. 5, July 1946, p. 143. Mayer uses a sequence of four increasingly deep cut-and-turn-over actions to force the top card. Not long after this, Fred Braue published “Little Card Rise” in his column in Hugard's Magic Monthly, Vol. 6 No. 8, Jan. 1949, p. 501. In this trick, Braue married the Mayer force with Sid Lorraine's miniature-card pop-up production that was first explained in The Linking Ring, Vol. 8 No. 1, Mar. 1928, p. 33, “A Novel Card Discovery.” Braue's explanation pared the cut-deeper force down to two cuts and turns. Thus it seems Mayer deserves credit for the cut-deeper force, with the two-cut handling following shortly after, its conceiver as yet undetermined. Fulves supplies further history and variants in the Prolix article cited above.
There is also a related force, where the spectator cuts off half the deck, turns it over, and drops it back onto the talon. The magician then secretly turns over the entire pack as he spreads the cards on the table. The first face-down card appears to be where the spectator cut, but it is the original top card of the deck. This force is commonly attributed to Bro. John Hamman, probably due to it being described multiple times without credit in his book, The Secrets of Brother John Hamman, 1989, p. 65 and 99. The force, however, was the creation of Lynn Searles, who published it as “The 'So Simple' Force” in The Jinx Summer Extra, 1936, p. 135.