As of tonight, this is almost done. It is now possible to modify the open state of existing discussions. For these, the option is added to the icons next to the discussion title.
I still need to handle closing discussions that aren't created yet: such as the "main" discussion when it has 0 comments, and un-started admin-defined topics; because there is value in disabling comments for a page without having to wait for at least 1 comment.
When that is handled, the same interface will make it possible to block users from creating custom discussions for a page, even though the area allows it. This option is added as an icon next to the "Discussions for Page" heading. For this reason, users who can block/unblock custom discussions will always see this heading, even if there are no discussions under it. Previously, the heading was hidden if there were no discussions.
Note that some discussions might already have a dormant closed state that was received from the importer, if the discussion was closed in the original database before it was imported. When the ability to close discussions is activated by the next release, these discussions will now be treated as closed. This might be jarring if you or your users were used to the discussion being open. Please re-open the discussion if you want it to be open. This is not a bug.