Dixie I think your hair would curl well naturally if you let it and helped it out a little bit...
I think your straight bits are probably deceiving, you probably won't be able to achieve tight spiral-y curls from those pieces but I think definitely you would get waves/looser curls.
I'd stop brushing, on the days that you want curls... brushing is just going to break up the curls and, like you said, helps some of those pieces straighten out.
Styling products are your key.... not that it takes anything fancy or that it has to take a lot of effort, there's just a couple things that really make a difference. For myself. I shower, wash my hair like normal. When I'm done with my shower I flip my head upside down. I get a good dollop of leave in conditioner and rake that through my hair (I alternate between Kinky Curly Knot Today and Mixed Chicks). Then I get a glob of gel (which again, I use Kinky Curly's gel... I like their stuff lol) and just scrunch if through my hair. Finally I use a microfiber towel or cotton t-shirt to do one last scrunch to get out the excess water and whatnot.
That's it. I try to add lots of moisture and the gel helps the curl hold (and also fights frizz). But just scrunching through a couple extra products at the end of my shower makes allll the difference.
This is an old picture from when I had no idea how to live with my hair. This is just brushed and air-dried. It's a rare shot too because I used to either flat iron it or put it in a pony tail... I never wore it down and "natural"
Aaaaand with a few simple changes... we have curls!
(sorry the picture sucks, I was like leaning back and just... at a weird angle.)
This was longer than I intended.