As I understand it, you want to remote control the computer you're FXPing from?
If you want remote control then
TightVNC offers that functionality for free.
Windows XP Pro also includes the Remote Desktop feature which is faster than VNC. Windows 2000 Server/2003 have Terminal Services.
Since you would be controlling the computer, why shouldn't they just give you the IP and username/password for the FTP sites so you could download it yourself...
A better feature to add would be SFTP support (SSH).
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