Mine is also huge pouffy and Hagrid like, and heat tends to make it break. So I have years of experimenting with mine!
Are you thinking of going full on "curly girl" natural curly? If so, you will be staying well away from sulphates, silicone and heat, so everything I'm going to suggest will not fit in with that. Fwiw, I tried curly girl for almost a year and gave up, it looked shit!
If, however, you have no strong aversion to silicone, know how to use a clarifying shampoo to avoid build up, and don't mind blow drying your hair, there are some products you could try. One thing I would suggest, if you're going to go full on silicone product styling, try going a bit natural on your shampoos and conditioners - I quite like the Faith in Nature range, it avoids all that extra product and the sulphates in the shampoo will help clear the build up every time you wash. Just an idea.
I've found Creme of Nature Argan Oil leave-in conditioner on Amazon - you give it a good shake and spray it on damp hair, and it makes hair very glossy and smooth. It doesn't completely de-frizz I must say, but it makes it softer so I can leave it to dry and won't be gigantic, and don't have to beat it quite so hard with the straighteners to be presentable - just a quick run through.
My other recent find which is the best thing I've found in 20 years of frizzy hair, is Colour WOW) Dreamcoat. It's expensive but you can get 50ml to try from Look Fantastic for about £12.
I put the lightest of light sprays on damp hair, nothing else, then blow dried it with the nozzle pointing downwards and with a brush. It is AWESOME. Keratin treatment in a bottle with none of the hassle, my hair is still wavy but it's smooth and non-frizzy! I run the straighteners over any flyaways and that's it. Unbelievable!
Many Amazon reviews talk about waxy build up, or it being too heavy - so I'll just take care not to put too much on, only use it every 2-3 washes, and clear the build up with a proper clarifying shampoo maybe once every few weeks if it's looking dull and heavy. But so far, so brilliant - give it a try! There's a thread on it, something like "Thinking of a keratin treatment, try this first".
Failing that, do you have £££s to spare? Brazilian blow-dry or keratin treatment at a salon, my medium length hair cost me £160. It's lovely, you get super glossy smooth hair and it's supposed to stay on for up to 4 months - but I only got two out of mine, and you can't use any products with sulphates. You can do your own at home (there are kits with good reviews) but even I'm too lazy to paint the stuff on then straighten sections of hair over and over for hours. Not one got time for dat.
Well that was long, that's because I've had the same struggle for so long! Good luck.