Yeah, I'm pretty sure Aussie Moist has a silicone in it. Is this the spray you use? Because if so it also has a silicone in it. Curls Marc Anthony Curl Booster Ulta.com - Cosmetics, Fragrance, Salon and Beauty Gifts
It would probably be nice to get a coco betaine shampoo, especially if you want to keep using the cone products. You can't be completely Shampoo free and use products with cones. They will not cowash out of your hair, and you will get build up.
If you have fine hair, I wouldn't cowash with something so heavy. I would consider Aussie Moist to be a rinse out conditioner. If you want to incorporate a shampoo and keep using Aussie, you should switch between TN and Aussie. Both together is probably overkill. You might be better cowashing with Suave Naturals conditioner or maybe VO5 conditioner. That much conditioner might have left you a little overconditioned.
Also, you might just need definition in your hair. You say you dislike gel, but have you tried scrunching out the crunch when your hair is dry? Like, after your hair is mostly or completely dry with gel in it, you can scrunch your hair to make it feel soft like it doesn't have gel in it. Then, you maintain your style and definition, but your hair doesn't have that hard wet look. If you don't like gel, then maybe mousse would be nice? Either way, a lot of curlies find that adding product is better on soaking wet hair instead of damp hair.
Here are some helpful links:
How to Follow the Curly Girl Method
Curlies on a Budget