My memory isn't faulty at all. I well remember the tenor of the times. It was the beginning of the feminist era, when "I am Woman - hear me roar!", was the theme of the day.
The appellation, Ms, was invented to elevate the status of those proudly unmarried feministas who'd grown past the debutante 'Miss' phase of their lives.
Suddenly, they were no longer 'old maids', but Fiercely Independent Women!, who didn't need a man to define themselves, or their place in the world.
You’ve got it all right except for the age link. Young females and some married women adopted “Ms.” as well. It was not meant to add another marker for unmarried women, but to remove such markers altogether.