One thing you could do is this:
- give the header div position: relative;
- move the image into the header. Give it position: absolute, right and top coordinates (eg top: 400px; right: 0; ) and give it z-index: 1;
- set the UL to position: absolute; z-index:10;
Worth a try, anyhow. Worked for me in testing, but might need some fiddling.
EDIT: gulp! Paul's solution is so much simpler!