Do you have the option of using rsync? At least this way you could resume if there were any issues.
If not, there is also a program called ftpcopy which would allow you to copy the files via ftp however it has the ability to resume and read timestamps so if there are any issues during the transfer you can run the command again and it will pick up where it left off.
Since you can't ssh, you are unlikely to have rsync. One alternative is to use a FXP capable FTP client (example FlashFXP) and do a server to server transfer. Note that this is dependent on the ftp servers supporting it. But it's worth a try and it can take over the role of comparing files and transferring only incomplete or nonexistent files.