You'll get these kinds of errors if you use the drag-and-drop copy within Windows explorer.
However, if you use Robocopy, you should find that you can copy the files without any issues.
The command-line version of Robocopy is built-in to Windows 7 and Windows Server 2008; it can be downloaded for other operating systems. Although there is a downloadable GUI, it's best used from the command line (aka CMD.exe).
By default, Robocopy should handle paths greater than 256 characters (there's a switch to turn it off, but in your case you don't want to do this).
Example command line (which will copy all files in the folder C:\Projects to the folder Z:\Projects):
robocopy "C:\Projects" "Z:\Projects" *.* /COPY:DAT /E