File is too large for destination file system - Already NTFS

So, after a lot more searching (I find it difficult to locate help for specific Citrix issues), I found a Citrix help page that actually describes my issue: http://support.citrix.com/article/CTX134844. It is specifically a Citrix issue, unfortunately, and the page does not provide a solution.

As some of you noted, the magic cutoff size is 4GB, and this is just a limitation of the XenApp service we are using, regardless of the file systems in place-- the error message is not accurate.

In order to copy these large files, I believe that I will need to find some other service (like a cloud storage location) or gain physical access to the server and copy the files to an external drive there.

Thank you to everyone that helped me troubleshoot this frustrating and time-consuming problem!