The mod says that you can disable and enable the mod through an existing save without causing problems, however for me this isn't the case.
I have a multiplayer server that I play with my friend and I wanted to disable spidertron but as soon as I save the game, disable the mod, relaunch and start the server up it instantly crashes my game.
Your log isn't showing any crashes so I can only assume that you are running into a bug in the base game that occurs when you load a save after changing the size of a spidertron. You may find that if you all get into a train (or enable the setting to allow getting into any vehicle) so that there are no spidertrons on the map then it might not crash. Or wait for factorio 1.1 which will fix the crash.
So my friend and I hopped into a train. With the weird thing that when I got in the train I got in WITH the spidertron, my friend got in and it put the spidertron in but not him, it worked. Wow, never thought it would've worked. Hopefully 1.1 can fix whatever is causing this to crash.
