Okay so all you did was edit config,inc.php for the database server (IP)
No, that's not all I did, but that's basically all that was necessary.

Knowing what I know now, here's what I would have had to do:
Have server A set up on the same version of UBB as server B.
Change the security settings on server B to allow incoming mysql traffic from server A's IP. (First time I have found cPanel to be more value than detriment.)
Change DATABASE_SERVER value in config.inc.php on server A.
That's effectively all I did and it works now. Pretty cool really. It should make the switch very easy now.
That assumes that you're using the default (3306) mysql port. I really have no idea where the db port is set or would be changed in UBB. Maybe that's just something that never happens in mysql, but I do it
all the time with other db's.
So, in summary, here's the checklist/plan for the final migration and switch over:
Verify security settings on new server will allow mysql access from old server.
Drop and recreate an empty ubb database on the "new" server (easier than dropping all the tables.)
Close the board on the old server.
Double check I have all IP's from both old and new servers.
Change DNS entries in authoritative BIND server to reflect new server.
Tar up the uploads/avatar directory (everything else static hasn't changed since my initial setup).
Start FTP'ing the tar file. (Compression doesn't help much here.)
Follow
Gizmo's checklist to migrate the database (including compression of the tar file. bzip2 works wonders compressing the .sql file.)
FTP the file to the new server. (The first FTP should be complete by the time the bz2 compression completes.)
Untar the files directory on the new server and check (aka update) permissions.
Uncompress/tar and import the database on the new server.
Update the includes/config.inc.php file to reflect new file system structure and location of directories and new username/password for ubb mysql user.
Open the board on the new server.
Change includes/config.inc.php on old server to point to new server (DATABASE_SERVER value & new username/password for ubb mysql user)
Test. (Aka watch email waiting for complaints to come in.)
my eta: 1 Hour. Hopefully less.
Man, it looks so easy when I write it down like that.
