In the layout I'm currently working with the header is fixed on the larger screens only. You do NOT want a fixed header on a phone layout, so if you do this trick be prepared to combine it with media queries for best effect.
Looking at your current layout, your header being transparent is going to be a problem. You're going to need to "cut" your header body copy of the background image widthwise. You don't actually need to cut the image, but you will need to reference it twice. The body copy will need to be offset by the width of the header. I think this will be seemless. Then, your text can go underneath the background of the header image and appear to disappear into nothing.
I'm tempted to try it just for the challenge, but I'm also pretty certain it will take a good six hours for me to get it to work.