It looks like ironsoul's suggestion of "Scripts->Partners->Dimension3D->Batch Imp Exp" works pretty well! The only thing is, it doesn't appear to get some of the clothing textures for some reason:

I don't really see the advantage of Scripts->Utility->collectSceneInventory other than if I wasn't able to find the textures in the first place. Also, collectSceneInventory dumps a lot of other objects into the folder that I don't need access to, like lights and cameras.

I'm going to look into wolf359's .fbx suggestion now...