If I was to close a section on in this case a service I would post an announcement explaining the closure and then lock the forum and keep in public view for about a week then move all the topics to the rubbish bin section of the site and delete that section.
That way it is a gradule removal and all your active members have time to adapt.
Delete the forum and all the posts inside. I am not scared of my post count dropping.
Recently, I emptied a hidden trash forum with nearly 20,000 posts in it (nearly 2 years worth of accumulation).
Because having large amounts of useless & discarded posts hidden away serves no purpose, especially promotion forum service requests. It may make the forum look better until someone figures out that there is thousands of posts unaccounted for. Everyone understands there is staff discussion forums but once the number of hidden posts becomes extremely large, members are going to sense something fishy is going on.