Thanks for all the responses!
Firstly, these are very compact files - 40-60k maximum. Luckily I know how to play the "crunch game."
All the sites are normal HTTP sites - I have the wimpy firewall that is included with the stock Win XP package but I have attempted to upload the files both with it activated and shut down.
I do have some webspace kicking around so I suppose I'll have to go that route - it just REALLY bugs me not knowing what the solution is! :x

Well, I have Windows firewalll shut off and I'm using Zonealarm. If I were you, I would attempt to upload something somewhere PRIVATE if possible. That way, you can establish that you are capable of uploading and these public sites are at fault. Since you have some webspace, I'd use that for the experiment.