After trying to create new saves under both Campaign and Sandbox mode: I still couldn't make any progression past the section to build the SI Drive. The first annoying bug was every time I'd load up the game the solar system would change, effectively causing all ships heading towards or away planets to be locked there until I got lucky to find a game with said planet in it. After that nonsense the next problem quickly appeared which is the reason for me making this guide for y'all; the bloody SI Drive is stuck in a perpetual Charging state and none of the game modes can overcome this. Now I couldn't find anything on the internet to remedy this, but after some trail and error I think I've fixed it.

To start I used the other guide on steam to get access to the command console so I won't go to in depth in this guide, but I'll explain how to solve the issues I've had.

To Fix the ever changing planet names you need to access the console:
Press ~ in game followed by: addplanet (put the exact planet name that your ships are headed to)

For example: addplanet OmicronPersei8





To fix the drive type in the console:
campflag
This will tell you how far in the "campaign" you are; this works with sandbox mode as well, now follow up with increasing this number by one. This is and example of mine:
campflag 12 (the SI Drive mission)
campflag 13 (Act II The Rugora System)

I believe this will work with any issues with story progression, good luck to everyone in this broken ***
game and hope this helps.