In case anyone comes across this with the same issue; it was a case of the DB dump being too large for MySQL to handle without timing out.
I found a free application - SQL Dump Splitter - that will allow you to break out into smaller files that the server can cope with. It will split the contents into table structure & data.
Install the structure first, and then for each of the value files created prepend with this code:
SET NAMES utf8;
SET @OLD_UNIQUE_CHECKS=@@UNIQUE_CHECKS, UNIQUE_CHECKS=0;
SET @OLD_FOREIGN_KEY_CHECKS=@@FOREIGN_KEY_CHECKS, FOREIGN_KEY_CHECKS=0;
SET @OLD_SQL_MODE=@@SQL_MODE, SQL_MODE=\\\’NO_AUTO_VALUE_ON_ZERO\\\’;
SET @OLD_SQL_NOTES=@@SQL_NOTES, SQL_NOTES=0;
And at the end of the file add in this script:
Then upload through phpMyAdmin / CMD as normal.