File name(s) too long for destination folder on file share migration.

So I'm trying to move some data from an older system running Server 2003 Standard to a newer one running Server 2012 Standard R2. Both domain controllers right now (the 2012 server is new and was recently promoted to DC; the old server will eventually be completely decommissioned).

The old server is mostly just a file server. What I'm trying to do for the majority of file shares is a simple copy/paste over the network from old server to new server (after making sure the files/folders on the old server aren't currently being accessed). Problem is, in doing that, I'm getting the "file name(s) too long for destination" message on several of the files. And yes, there are quite a few files on here with really long names, but we're talking about a directory structure with hundreds of thousands of folders/files under it, and the only option I get when the above error pops up is to skip the problem files, which I obviously don't want to do.

Is there some way to just automatically truncate the filenames during the transfer or something? I feel like this should be fairly simple, but I can't really find anything that can automate what I want to do.