Hmm - if verifyFactionData() threw an exception, that would be in the log, and this is not it.
At some point on startup, the game gets all the ModPlugins from the enabled mods into a list so that it can call their various methods (such as onGameLoad()) as needed. The first element in this list is the plugin specified in coreLifecyclePlugin in settings.json - the core's version of the ModPlugin, since the core also needs to do things in response to the same kind of events (onGameLoad()), etc.
The part that's failing, according to the exception, is trying to create a new instance of the class specified there, see:
Failed to find script of class [com.fs.starfarer.api.impl.campaign.CoreLifecyclePluginImpl]
The full classname appears to be correct. I'm not sure why this might happen. Some possibilities:
1) The actual class file is missing or corrupted
2) The class does not have a default constructor (it doesn't, but it also doesn't have a non-default one, so that's fine)
3) The default constructor throws an exception (I think the error would be different, and also see: it not having an explicit default constructor anyway, or any initialization code that might fail)
#1 seeming the more likely, that's why I'm recommending a reinstall of the game. It's not getting to the point where it'd try to verify faction data; that would be when you're loading an actual campaign game.
It's definitely mod related. The game loads and plays just fine without this mod enabled.
I'd still try a clean install just to rule issues with the base install out.