How can I force the formatting so that the Filter by Committees check boxes section is always above the results? Or to the side? Can I force the check boxes into 2 columns?
You have multiple options here. If you use any page builder, then you can use their building blocks to put the settings and the results shortcode there.
If not, then there is a shortcode generator, that lets you create a custom layout for the search/settings and results boxes.