I never did find a way to make the header transparent, but I did come up with a workaround.
I wrapped the entire contents of the header.tpl file in a div, and used the same image as I used for the main background, and then I made both of them static. It's still not transparent, but for all practical purposes the visual effect is the same.
In case anyone needs this is the future:
...in custom.css
#wrapper { background-image:url(whatever_image_you_got.jpg); background-repeat:no-repeat; background-position:right top; background-size:cover; background-attachment:fixed }
...and then in a the div that surrounds everything in header.tpl
<div style="background-image:url(same_image_as_you used_the_first_time.jpg); background-repeat:no-repeat; background-position:right top; background-size:cover; background-attachment:fixed"> </div>
...this solved the problem, and I probably would have thought of it sooner, but I was I too headstrong on making everything transparent as opposed to actually achieving the visual effect.
This was much simpler, and a whole lot less headache.