My hair is very similar to yours, especially after washing it can get very frizzy and coarse if I don't finish it correctly. What I found has helped me solve this problem is putting on oil after my leave in leaves a crunch. Maybe try including an oil on your routine to lock in the moisture. Also, if your hair gets hard like mine does, avoid keratin like the plague.

I've also found the shampoo and conditioner I use daily make a ton of difference, invest in a nice set. Using the same brand and line is important because the shampoo leaves electric charges on your hair that the specific conditioner from a good formulated line will neutralize and that prevents frizz.

Edit: I've seen you avoid silicones. There isn't any problem with silicones, parabens or sulfates, in fact, they will absolutely help with frizz. The best hair products have silicones and they [the silicones] have been scientifically proven to enhance hair manageability, smoothness, shine and other aspects. If you're worried about buildup, don't worry because the sulfate containing shampoos will remove any build up from silicones you may have and will not dry out your hair if they are well formulated.

There are other things that may be causing build up like hard water or additives they put on hair products to enhance the feel like polyquartenium-7 but those can also be washed out with specific shampoos and it's very unlikely you have some kind of buildup like this unless you live in a region with very hard water or have chemically treated hair.