Fastpitch: Batter's Location in Batter's Box Compared to Plate

[SoftballGuy247]

As a longtime coach (15 years) of fastpitch softball and player (15 years) of baseball, I was taken aback the other day when I realized that for all this time I might not have truly understood the strike zone. I would ask for some of my expert umpires to assist in clarifying the following scenario:

Batter stands in very back of batter's box, thus putting home plate in front of the batter's front leg/knee. Pitch is delivered by pitcher, crosses the plate within the knee-to-armpit strike zone, but then falls out of the zone below the front knee of the batter.

My question is this: Is the strike zone in fastpitch softball considered at what height the ball crosses the plate, irregardless of where it crosses the batter? Or does the ball need to cross the plate AND the batter in the strike zone?

I realize the scenario of having a batter in the very back of the box in fastpitch might be rare, but I would like to get a clarification so I can correct my thinking that may have been wrong for 30 years! Thanks all!