Hi,
You can scp the databases from one server to another... Do this on the server from where you're transferring the accounts.
Code:
cd /var/lib/mysql
scp -r CPUSER_* root@SERVER:/var/lib/mysql/
Where CPUSER is the cPanel user, and SERVER is the hostname or IP of the server you're transferring the accounts to.
After doing this, make sure that the folder & files are owned by mysql:mysql
If it's many users, you could try coping the whole mysql folder (Not sure if they are MySQL configuration files on it, so first make sure they aren't)..
You should open a ticket about the transfer script issue.