Ok, so I dug around a bunch and found this which is super natural (no sulfates, parabens, silicones, etc and no aloe vera or coconut (both don't work great for low porosity hair) or heavy creams/butters. You just need to find a Trader Joe's near you. Trader Joe's Tea Tree Tingle Shampoo & Conditioner https://www.amazon.com/Trader-Joes-Tingle-Shampoo-Conditioner/dp/B004IM0KYM
I feel like this could be a good fit, but I would also try the shampoo/conditioner you already have first! Also I have never tried this product before, but I think I remember seeing at least one post where someone used this in their routine, so maybe someone else can weigh in, or you can search the sub for mentions of it. Let me know how it goes!
1:10, I have used Head and Shoulders before, which did not work. Nizoral kind of worked but I was concerned about the long term use, what I do now is use this oil one hour before I take bath and I use these shampoo and conditioner combination
https://www.amazon.com/Trader-Joes-Tingle-Shampoo-Conditioner/dp/B004IM0KYM
Trader Joe's sells a sulfate-free tea tree oil shampoo! Super cheap in- store, much more expensive on Amazon. http://www.amazon.com/Trader-Joes-Tingle-Shampoo-Conditioner/dp/B004IM0KYM
You are right that SLS is the best cleanser out there.... that's why it is the first ingredient in Dawn dishsoap! However if you tend to have dry hair already, you might not want to use such a harsh cleanser because it will continue to dry your hair out. This can be "solved" by applying silicones afterwards, but the silicones are really just covering up the problem. Then the silicones build up unless you use an intense cleanser like SLS, and you are stuck in a circle!
What I would recommend is gentle cleansers and silicone-free products. Unfortunately TresEMME doesn't make a sulfate-free shampoo (that I can find, anyhow) but there are other options, like this shampoo and this conditioner.
This information isn't of my own discovery... it's following something called the CurlyGirl method, which is a hair care method for wavy and curly hair. There is a whole subreddt r/CurlyHair with tons of information! Check out their sidebar for product recommendations, discussion of sulfates and silicones, and other neat stuff, if you are interested! I don't find the CG method to be limiting... there are still tons of products to choose from, and my hair has definitely been way happier.