Two thoughts, maybe you could use the Redirection plugin to redirect the specific links you want on a second home page.
Is a second home page necessary? Your main listings page doesn’t necessarily need to be the directory home page. The page that you have the before and after content with multiple Connections shortcodes is the main page that you link to in you menu but the Connections home page could be another, maybe a sub-page, where all the links resolve to and only have the Connections shortcode. The net effect would be two “home pages”. Would that work?