The FTP password is for authentication on the target FTP servers: the password unlocks access to the storage service of these servers. To a large extent, this is their problem, not yours.
To be more detailed, whenever you send a data file to a server, the overall confidentiality and integrity of the data is partly the responsibility of the server's administrator. You cannot make the data more secure than what the peer is willing to achieve, and, by insisting on FTP with passwords and data sent in the clear, the servers' administrators are demonstrating that they do not care much. The password they give you is a delegation of responsibility: they grant you an access and may require some extra protection measures for that, but if they do not, then it is not your role to unduly insist on the subject. As they say, don't try to be more catholic than the Pope. By raising the issue of the insecurity of FTP, you have fulfilled your duty of warning the unwary; from that point, it is up to them to follow up on the subject.
Practically, you might want to take some steps to avoid leaking the passwords on your side, e.g. read-protecting the configuration file which contains them. This is not really to make the system more secure, but rather to avoid becoming the scapegoat if (when) the system is hacked. You then need to show that your end of the protocol was not the weakest point, and since FTP has no encryption and uses cleartext passwords, that's not hard; encryption on your side would be overkill. Also, if the system on your side must proceed unattended, then this means that whatever encryption is applied on passwords can be reversed automatically by your machine, so any encryption you apply would not, theoretically, be stronger than plain read access restrictions on the configuration files. So my counsel is: don't bother with password encryption, it would give you much complexity than real extra security, and that's not the weakest part of your system anyway.
Of course, you might have to ask yourself whether you really want to push your potentially sensitive data to third-party FTP servers whose administrators have demonstrated, by refusing to switch to a more secure protocol like SFTP, a rather disturbing amount of carelessness with regards to security issues. It all depends on whether the data you want to push is really sensitive or not.