Couple of things may lead to the right method, but as far as automation, not so sure that there is an instruction to provide "automation" of the transfer.

In a way doing an upgrade of the site, though it will be on a different server, so that's where caution should be taken in doing this as you may find yourself trying to track down a problem related to operation when it was the upgrade that caused the issue, or a file didn't get fully transferre, etc... The typical suggested upgrade instructions would be: http://www.zen-cart.com/entry.php?3-...d-of-upgrading

Then there is instruction here for moving servers:
http://www.zen-cart.com/content.php?...fferent-server

One thing that has been improved upon is that if you create includes/local/configure.php file and admin/includes/local/configure.php file and not have a version of those in the includes/ and admin/includes folders, then when transferring files if you omit the local directories, the old files are overwritten with the new but the configure.php files are untouched. :)

There are several other aspects to consider, but that may be a start. Glad your other issues got fixed. Congrats!