Well, that is what my host site did: cloned the Classic board on the new server. However, when I try to log into the Control Panel on the cloned board, it immediately throws me into the old board (I can see that from the url.)

Currently the only difference in the URL is:
old: http://www.mysite.com <--mysite is just an example
new: http://www2.mysite.com

I think the control-panel's throwing me back to old site is due to the paths & urls on the cloned site pointing me back to the old server. Say... is there a flat file I can edit to change them???

...It's late here... I'll check back in ~ 9 hrs. Thanks for all the suggestions.