What I want is a pith helmet or full-brimmed hard-hat style - a stiff, curved brim that goes all the way around - but suitable for bicycling. There's nothing out there that I can find. I've actually considered a real pith helmet, but the way the harness of that is anchored inside of the helmet, doesn't look like a very steady, secure fit.
I just ordered a new bicycle helmet, a Kali Lunati Sync. It seems like the quintessential MTB helmet. I chose the colorway that liked the most. Looks fine to me, I just wish it had a more functional brim.