Almost all of your code is correct. I didn’t even know about the insert_with_markers function, and now I do, so thank you.
In return, I believe I have your solution.
get_home_path() is not defined when any of the hooks (init,wp, etc.) you mentioned are triggered. That function is defined in the admin-side “file.php”, which as part of the admin dashboard side of things, has not yet loaded.
The hook admin_init, however, should serve you well, presuming you are making those .htaccess changes on the admin side. If not, you could either include wp-admin/includes/file.php manually, or use an alternate way of finding .htaccess, such as the constant ABSPATH (although they are not equivalent).
Using the admin_init hook on the first function you provided, I found the rules written to my .htaccess file the next time I loaded a page on the admin side.
By the way, you might want to do a check for current_user_can( 'edit_files' ) before allowing that code to run.