You have to switch 5. and 6.
All hosts entries and the external DNS records need to be in place BEFORE you run the install script.
As a general tipp for the Server-Migration:
Set your DNS Records TTL from the standard 3600 down to a very low value like 60.
Do this right NOW before the switch, because in the meantime the lower TTL value can propagate.
All DNS Servers learn that they have to check for new values every 60 seconds,
which makes it easy for you to do a quick switch (and if something fails, a quick switch back).
After a few days - if everything went fine - you can again set the TTL values up to 3600 if you wish.
I learned it from this article:
http://www.simplefailover.com/outbox/dns-caching.pdf