For a "legionaries style" hat, you may want to look at a Frillneck (aka Araphat). I bought this originally for kayaking but also use it for walking. I believe the Adapt-a-cap (which is at BCF) is similar but does not use velcro.
What I like about the Frillneck is the amount of coverage you can get depending on your circumstance (right up to only exposing your eyes if you need to go to this extreme). This page has examples (
http://www.frillneck.com.au/catalog/howtowear.php). I normally either wear it covering the back of my neck only, fixed at the front to cover the top of my chest/neck as well (good if it is windy) or - if it is not sunny - run the flap through a loop at the back to keep it out of the way (like a pony tail). If it is *really* windy it has loops that allow you to add a chin strap (I have not bothered doing this).
It obviously a little more stuffy than a normal broad brim hat on a hot day without air movement however I regulate the temperature by wetting the entire flap regularly if it is really hot (so I do not use a bandana/buff etc). While you can wrap your head up well, I still use a bug net as normally if you are worried about something like flies, it is normally too hot to do this.
As for being hot in long pants, I have a couple of pairs of Columbia Silver Ridge convertibles. They are very light, UPF rated while they could be a little more hardy (I have had to patch them a few times) I have never felt they were too hot to walk in. Even if you get something a little less delicate and possibly a little more on the hot side, if they are convertibles, you at least have the option of wearing them as longs when it is suitable and shorts when it is not. I have recently ordered some Prana's which will be more hardy but I suspect not as cool to walk in (but I plan to do the OLT next year so this will come in handy).
Another thing I have done is grow a beard to help provide some extra protection to the lower part of my face and under the chin. Being clean-shaven all my life It drove me bonkers initially but I believe it has been worth it. I did this to help protect again the reflected sun off the water due to all the paddling I do but I think it will come in handy for walking too. While I still use sunscreen it is normally only on the nose/cheeks/forehead/back of hands (if not wearing gloves). I tend to use less cream and reapply less often than I used to mainly as previously I was so horribly paranoid about getting burnt (again!) that I would over-do it, leading to the "greasy, disgusting, oily mess" at day's end you mention.