Maybe if you can find a mid 90s copy of CuteFTP or the like, your line will deal with it a bit better. As to whether an old and simple piece of software will be able to deal with the problem any more so than a contemporary one, I don't know.
BenF was telling me that Steve Bromley (I think he said his name was) works at something like an Arctic research station. Maybe he could put you in touch to find out what exactly this software is.
As a more immediate and better option, I'd get a line test and see what the engineers make of the results. Threats to leave your ISP and/or phone provider usually result in a better standard of service (sadly).
If I can think of any of the other applications I used to use for file transfer in the mid 90s, I'll let you know.