"What do we make of the "Turbolift 7" signs?"
Difficult to answer, maybe we should first try to determine how many different turbo lift numbers did exist in TOS (right now I can't think of more than 2, 3 and 7).
My pet theory (for the moment) is that it tells the passenger that turbo lift 7 could make stops at 7 different locations or deck levels.
"Mudd's Women" walk counter-clockwise to turbo lift 7, exit on deck 12 and continue to walk counter-clockwise to Kirk's quarters (a few counter-clockwise steps forward and they arrive at another turbo lift 7 (used by Kirk and Spock in "The Enemy Within").
If that were the same turboshaft # 7 their movement would have most likely been different.