Hey there! This sounds like a really cool idea and I'd love to help this fan project get off the ground.
As coyot said, you can use the modding engine to export all the game's data, including the cutscenes, see this sub-forum:
One caveat, however, is that I think the mod system won't currently load custom audio. I can add this in the next patch if you want it, though.
The game wasn't designed with voice acting in mind, but it's flexibile enough that once I add custom audio support you could add it just by recording the lines and tweaking the data. If you look in scripts.xml, you'll notice certain tags where a sound effect is played, like an explosion, etc. All you would need to do to add recorded voice lines is create the files, then add a sound effect tag with the right sound file id at the point where you want the dialogue line to play.
I would need to add a little more support to make this work smoothly - right now, sound effects will trigger and play, but if you hit back or forward they won't cut off. So if you were to put in dialogue-as-sound-effects, then mash "next" and/or "back" repeatedly you could easily get dozens of dialogue lines playing on top of each other all at once. What you'd want instead is for it to halt all other dialogue lines playing and only play the current one that matches on screen dialogue. This would be simple enough, I'd add an attribute to the sfx tag for scripts.xml, something like, "dialogue="true"" or whatever, and make the game treat that differently.
You could start recording your lines and putting in the sfx tags now, and then I'll work on getting the extra functionality you need in the next patch.
When we get Steam Workshop integrated with the game, you could distribute your mod that way.