I think I should think of giving up

[DrByte]

PHP Warning: mysqli_query(): MySQL server has gone away

It's very possible that hosts haven't tuned their defaults as well as they had with the older mysql stuff. Or the defaults are just stricter and need tweaking where tweaking wasn't needed before. The tweaks could be to both the php.ini (for PHP server side) and the my.cnf (for MySQL server side)

Any idea as to what those tweaks might be Dr Byte?

Googling for the error message "MySQL server has gone away" brings up tons of articles suggesting various server-side tweaks:
http://stackoverflow.com/questions/1...large-sql-file
https://dev.mysql.com/doc/refman/5.0/en/gone-away.html
and lots more

Another possibility is that in your Zen Cart site you might have added custom code to prematurely call application_bottom.php or otherwise close the session and/or database connection, in which case simply "not" doing that would be advisable.
And of course using old versions of any ZC code files copied into a newer-version site can cause undesired effects.