Game keeps randomly crashing within 40-60 minutes into a game

Right-click on stellaris.exe, properties, compatibility. Tick "disable fullscreen optimizations" untick every other box in that dialog, Apply, and exit.
Then in the launcher Game Settings menu, select the fullScreen display mode, Vsync off, refresh rate 60.

Then test with a new unmodded galaxy, NOT any existing one.

If that doesn't help:
DXDIAG is a program you run from the Windows search box on the task bar. After running it will open a window and start collecting info with a progress bar in the lower-left corner. When it completes click the 'save all information' button and save it to a file then attach that file here.

Please attach here your Documents/Paradox Interactive/Stellaris/settings.txt and pdx_settings.txt .
From your Documents/Paradox Interactive/Stellaris/logs/ folder, attach here system.log , error.log , exceptions.log  

We see some crashes in stellaris.exe in that dxdiag, so it is a little surprising there is no exceptions log.

After. a crash, can you reload and play on? Or do you need to wait or reboot?

What fps do you see in the game before it crashes? Anything over 60?

Please report the temperatures of your CPU and video (GPU)
1/ before starting the game up and
2/ after say 30 minutes' play.
If your PC's vendor has given you no way of reading temperatures, install
SPEEDFAN http://www.almico.com/sfdownload.php  

Setting the refresh rate to 60 ought to limit the fps to 60 also. How you are getting to 600 I cannot understand - is perhaps GeForce Experience running? If so it may be overriding the settings we did before.

And, as your Windows desktop is 60hz you are okay to turn Vsync on for this game again. That really should limit it!

We see temps up to 77c there, perilously close to the 80c mark where things can start going seriously wrong. We need to get that down!