I found a solution, although it might not be the best one.
In header-extensions.php, under the area that “shows the site logo, title, description, searchbar, social icons etc.”, I deleted whatever social networking site I wanted to get rid of in the array (ex. $options[ ‘social_pinterest’ ]). This got rid of the icon in the header without leaving any extra white space while still making the ones in the footer functional.
Figured it out.
I created a Home link on my navigation bar and, in the custom css area, made that into my logo using this tutorial: http://diythemes.com/thesis/rtfm/replace-wp-menu-text-links-image-sprites/
Then, I moved the not-home links (using their id numbers) down to where I want them.