After digging around relentlessly, I've been able to come up with a solution, many thanks to a chap on GitHub who published the following npm package electron-forge-plugin-dependencies.

Instead of installing the npm package, I've decided to manually add the code into my project. Pasting the solution in here would make for an answer far too long, so please refer to these changes I've made in the repository linked in my original question. I will keep this repository up until the end days for anyone that might wish to use it as a starting point for an electron application built using forge with SQLite3 and sequelizer.