I’ve never thought of myself as having a large head (although I do have some hair) - I have a Patagonia Duckbill hat that works very well for running aside from one considerable flaw - its too small. I can place the hat on my head but the combo of running and gust of wind threatens removal.
Any recommendations on a similar hat that provides a bit more head volume?
They’ve got a few different models, I do have a big noggin. They’re adjustable and come in different sizes. They’re also often on sale.
I have a Sprintz hat for running. I’m not sure of their size range or the circumference of your head—you’ll have to measure/verify that for yourself.
When it’s windy, I do flip it around backwards to avoid the bill catching the wind. I also find that flipping it backward routes sweat to my back, rather than down my face,
Outdoor Research’s “Swift” cap is the best-fitting one that I know of. 
This x1000. I have several in black and white. Washable, too.
Not the most stylish but the click all the boxes. or has some good hats with sun protectant panels that come down as well.
I’m a big fan of Janji’s hyperlight cap. Super lightweight, washable, and haven’t had an issue with windy days despite having a largish head. I have multiple in a variety of colors.
https://janji.com/products/afo-hyperlight-cap?variant=51940474847595
How about you give some of your skull to me? My head is too small for hats. We can balance things out.
Janji is great too!
I’ve got their trailbreaker cap, which is probably my #1 for casual use. 