These are huge issues for me, too.
Blowing away: The best strategy against is almost certainly a chinstrap. But I hate
having anything touching me under my chin; it makes me feel like I'm choking. So I'm trying to work on some different strategies this year.
My wide-brimmed hat has a band of ribbon sewn around the inside. Normally, it sits upwards, so it's totally tucked in. I noticed that pulling it down around my head gives a much tighter fit. I've decided to enhance that (and also make it less ugly) by sewing a long length of fabric to that band. This piece is about 4 inches wide and 4 feet long. The extra length hangs down evenly at both ends, at the back of the hat. This has a few different functions. First, the additional width will help the band to stay down against my forehead and increase its contact with my skin, for extra "grab". The additional length gives me some tying options: I can wrap it twice around my head and tie it in a bow at the back, allowing it to be tightened even further; I'm hoping this will be enough for ambient wind. Alternately, I can tie it at my throat; the angle it sits at, it shouldn't feel to chokey unless the hat actually comes off my head. Finally, I can put it under my arms and tie it at the back. This way, there's no chokey feeling, and if the hat flies off, it ends up on my back like a knapsack.
There's also the bonnet strategy: Tie your hat onto your head using a scarf. The scarf goes over the hat and ties under the chin.
Finally, if you have long, thick hair, a hatpin might work for you. I'm considering trying it, but my hair is only marginally long and not thick at all, so I'm thinking it's a pipe dream.
Sweatiness/hotness: Gah! This is possibly an even more intractable problem. I think you're right about the cone-shaped hat. Tall ones (think of a classical wizard's hat) would be good, too, because there's plenty of airspace up there. Definitely, wicker or something else with holes/mesh/vents so that air can pass through will help a lot. But I find that even with a hat that's tall and venty, if it's to grab the head at all, there'll be a band where it fits tightly, and there you will sweat. (And thus, my big-piece-of-fabric solution to the other problem has a major drawback.... more band = more sweat).
If you google "Yemen desert hat," you'll find lots of pictures of women wearing hats like this:
They're apparently excellent at keeping the wearer's head cool, due to the wicker and the extreme tallness. Also, they're beautiful. The whole outfit is gorgeous.
Again, though, there's the problem of securing it. I couldn't find any pictures that showed how they were doing this. Being desert people who do physical labour, they must have a way of keeping these hats on in the wind!
If you want drama to stop following you everywhere, try letting go of the leash.