BuddyPress.org

Sounds like you can do pretty much everything you want to do with 2 themes. One theme would be for the main site. The second theme would apply to all the subsites. With the theme you’ll be able to add links for users on the subsite to go to the main sites forum. In fact, with the theme on the subsite you can do incorporate whichever BuddyPress features you want them to have visible. You can either modify an existing theme or create a child theme from the default one: https://codex.buddypress.org/how-to-guides/building-a-buddypress-child-theme/

Depending on if you want the forums to be part of groups or not, you may want to investigate doing a stand alone install of bbpress or some of the global forum plugins I’ve seen mentioned.