Having a character that can approach quickly and lethally is a good thing, and I used to see the same thing from a lot of intermediate level Foxes and Sheiks in Melee because it works. It's fast and doesn't have much recoil time, and sets up for combos at low percentages. Against more experienced players, you will probably have more difficulty in relying on this too much, and you'll be forced to change tactics.
I recommend (if you haven't already) making your way over to the ZSS character board and posing the same question there, perhaps with your video evidence to back it up. People there would likely be able to give some sound feedback. And of course, watch as many good ZSS players as you can and watch how they approach based on the character matchups. Those two things will do you more good than I ever could, advice-wise.
Good job on the comeback!