Honestly I think you picked the worst possible angle to draw 2D from... I always dread doing stuff like that, it's so difficult to get looking good.
With top down you need to exaggerate, the hard hat would be bigger than usual, and you might only see a hat with some arms and legs under it, the further you get from realistic scales, the easier it is.
I would keep the character in 3 parts, hard hat at the top, torso with arms and finally legs. Animate these independently, so you could turn the head before turning the body, have a simple running animation. The one time I got this looking decent was when I broke it into 3 parts, had a Nico from GTA4 character, bald head, leather jacket etc, and independent animations. With akimbo dual wield pistols it looked awesome... maybe a bit like a stylised Hotline Miami.
Anyway, I would draw a yellow ellipse, then a smaller one inside, and add some subtle shading, try and think of the core features of a hard hat that make it recognisable from above. Spend some time on it but really you shouldn't worry a great deal about highlights, because the stronger and more obvious your highlights are, the worse they'll look when you rotate the hat. If you try and make it appear that the highlights are mostly from above, add drop shadows, and basic running animations to the arms and legs. If it works out like the Nico demo I made then you'll like it, and it won't be a daunting task to draw the arms and legs etc. Plus, keeping the torso and legs separate means you can interchange them, like different trousers and shirts, different hats etc.