Disable only the comment form/box itself?

The comments_open() function is used, both by core and typically themes to determine status for specific post. It has filter of same name for result, which you can use to manipulate it individually for the post.

comment_form() won’t actually output form if check is false and fire comment_form_comments_closed action in such case.

Native WP themes, shipped with core, are also good examples of building this check into templates.