The other space (or padding) that you’re seeing is coming from the widget area. Adjust the padding on line 2063 to around 20px and you’ll see that space shrink by half.
.header-image .site-header .widget-area {
padding: 20px 0;
}
Once you do that it should look like this – http://i.imgur.com/MkNVJIL.png

…..Which looks good to me. Let me know if you get everything working.