Here are a few methods that can be used if your looking for ideas:
The easiest way is to backup all your data to a 2nd HDD and coordinate with the datacenter a time for them to do a reinstall. The downside is you will have a few hours downtime and remember to coordinate with da to change your licence to the 6.x version.
A better but harder way which I used was to purchase another dedicated server installed with FreeBSD 6.1 and play with the DNS. Then I moved the accounts to the new server which will give you very little downtime. The only real downtime was when I moved the mysql data across to the new server but that can't really be helped. I used this method as I thought I may as well upgrade the server while i'm at it.