I've been trying to figure out a way to explain how I pronounce gestion, but there just isn't an English equivalent to the initial G.

Have you seen the movie Gigi? The way Maurice Chevalier pronounces Gigi with the Gs being soft. That is how the initial G is pronounced.

G - like Gigi,
es - like the ess in "less"
ti - tee
on - like the on in "only."