There is hope at the end of the tunnel.. so to speak, if you don't want to give up FlashFXP there are 3rd party SFTP to FTP tunnel applications that will bridge the gap between FlashFXP and the SFTP server. I haven't tested this but I hear it works great.
BitVise Tunnelier
http://www.bitvise.com/ftp-bridge provides a SFTP to FTP bridge, Tunnelier can normally be used free of charge if it is used by less than 5 people and on less than 5 machines in an organizational department.