There is no way to "directly" do this in Invision Community, but I have access to the raw database itself.
So I wrote a query that would take the table containing all of the forum posts, look for the old domain and replace it with the new domain.
MariaDB [m4mforum_ipb]> UPDATE forums_posts SET post=REPLACE(post,'message-forum.net','m4m-forum.org');
Query OK, 16209 rows affected (49.234 sec)
Rows matched: 1837117 Changed: 16209 Warnings: 0
That query changed over 16,000 old references within the board posts. I found a few old threads that should have had the old address and links appear to work now.
While this should not matter too much... just for documentation sake, this query only was run on the post database, so it did not change personal messages or indexes, etc.