Yes, it looks like you are headed in the right direction. I don’t have a lot of time to study it, but I see two distinct things you should work on first:
1) The colors of the gradient fill are off. I’m sure you noticed already, but you asked. How I match colors is make a small box they eye dropper a color and add it to my swatches – you can then choose that color in the gradient tool.
2) The outline of the letters in the original artwork is a much thinner outline, then a drop shadow added.
Hope this helps.
Steve Crook, Jr.
http://www.stevecrookjr.me
I am a simple creative professional that can get my Adobe suite and a few other creative tools to do what I want. Barely. 🙂