This is what I did, to get everything working.
1) Downloaded and installed Java from here:
https://java.com/en/download/manual.jsp and it's the third link down "Windows Offline 64-bit"
2) Made a new folder inside Starsector's directory called "jre8" so the file path to that folder looks like this:
C:\Program Files (x86)\Fractal Softworks\Starsector\jre8
2) Upon activating the Java installation .exe, check the box marked "Change destination Folder" and select newly-created "jre8" folder as the destination.
3) Install Java into that new folder.
4) Delete Starsector's original "jre" folder and rename the "jre8" folder to simply "jre" and run the game.
5) Play Starsector.
At least that's what I did. Also, giving the memory allowance half of your RAM (if you have enough, that is) might help. I have 32GB, so with an allocation of 16GB, it's pretty much guaranteed to never crash. Tempted fate though, haven't I?
EDIT: Damn. Missed a page when reading. And it's already been solved. Well, you can either ignore what I posted or use it for future reference. Whatever.