You mention: I'd like some of my posts to have their excerpts removed.
This cannot be done by WordPress or PageLines by default settings. Yes, excerpts may be removed, easily. However, to do so for some posts requires a plugin called Special Recent Posts which makes a post blog list using a shortcode, customized to specify what to include. It may be set up by category, so you will be able to tell it to list all the posts in X category with no date, and no excerpt, showing only the thumbnail, title and a link.
You also said "To clarify, all of these type of posts would have the excerpts removed, but not the ones at the top of the page that have the larger pictures."
This is possible with
because the shortcode may be changed and used again on the same page, to show excerpts.
If you wish to use the plugin in column mode, you can do this using the Grid System, placing the shortcodes inside grid elements.