OK Pete, you can follow below steps to migrate data of Edocman from old site to new site
1. Using PHPMyAdmin to export all Edocman tables of old version to .sql file. The Edocman DB table will have the prefix (#__edocman...). For example: jos_edocman_documents.
2. Open .sql file by Notepad and replace the prefix of old database by prefix of new database.
3. Import modified .sql file into new Joomla database site. Because in .sql file, you add option "Drop tables if exists", so even in new site, you already installed Edocman. You won't have any issue in this step.
4. Re-install new Edocman version in new site.
5. Copy all files and sub-folders of Edocman document root to site.