BuddyPress.org

No idea. Certainly is going to involve hacking something somewhere. I was going to suggest that you try changing the permalink_structure option (or filter $wp_rewrite) but, even if that worked, you’d still need to be be able to dynamically put the username into it, and then perhaps other links in BuddyPress might break (not sure).

I think a solution would involve changing the WP_HOME option or constant on a per-site basis. Off the top of my head I can’t think up a way of grabbing a sites’ “username” earlier enough to be able to then edit WP_HOME.