I did a search here, but didn't find any references to the 1981 "The Ideal Solution" booklet, which was one of the early solution guides for a 3x3x3 cube. There was also a 1982 Ideal solution booklet for Rubik's Revenge (4x4x4).
One algorithm in the book is called "Rubik's maneuver", used to flip (rotate not swap) a pair of edge pieces. Using Cu for center slice up and Cd for center slice down, the algorithm is Cu U Cu U Cu U2 Cd U Cd U Cd U2.
Making use of this algorithm allows for an alternate beginner's solution. Solve corners first (normal corner algorithms). Solve 3 of 4 top edges, solve 3 of 4 bottom edges (no special algorithm needed). Solve last pair of top and bottom edges (simple algorithm). Turn puzzle so solved top and bottom are left and right. Use Cu U2 Cd U2 to get one edge piece into place. Put that piece at the back bottom. Repeat Cu U2 Cd U2 to cycle (move) 3 edge pieces. Use "Rubik's maneuver" to flip edge pairs as needed.
What is the standard notation for a center slice move on a 3x3x3 (or any odd cube)?
Update - I left out the notation used in the old Ideal booklets. For the 3x3x3, the notation was English like: top left or right, bottom left or right, left up or down, right up or down, center left or right or up or down. For the 4x4x4, a generalized notation is used: "tables" for horizontal planes, "books" for vertical front to back planes, "windows" for vertical left to right planes. From top to bottom, tables are noted as T1, T2, T3, T4. From left to right books noted as B1, B2, B3, B4. From front to back windows noted as W1, W2, W3, W4. Tables move left or right. Books move up or down. Windows move clockwise or counter clockwise. A 180 turn was noted as "twice". Some old BBS abreviated: "up" "dn" "lt" "rt" "ck" (clockwise) "cc" (counter clockwise) "tw" (twice).