I solved this myself.
I turns out there was an issue with the server that was preventing Ghostscript from running.
We had PHP-FPM enabled on this server, which was preventing the php exec() function from running. Once I followed these steps and removed exec from the new settings for PHP-FPM, Ghostscript started working, and in turn Google Drive Converter. It's possible this will fix the Unoconv issues too, but I'm happy enough just using GDC.
https://forums.cpanel.net/threads/enabling-php-fpm-forces-disable_functions.590799/#post-2391379