OK, I completely re-did everything, fixing the things you stated. Here's the new URLs:
Platform: http://www.technicpack.net/api/modpack/currently-something-special
Details: http://www.technicpack.net/modpack/details/currently-something-special.458530
Modpack: http://downloads.twprogrammers.com/currently-something-special-0.1.zip
However I get the same thing, just with the new URLs. It even said "downloading currently-something-special-0.1.zip", but as you said it rewrites it.
UPDATE:
I opened the modpacks folder (%appdata%.technicmodpacks) and found that it had a 'currently-something-special' folder. I entered it and found the standard folders (mods, bin, coremods, ect.) and they were all empty, along with a non-empty 'cache' folder. It had the perfectly intact zip in it. I even MD5 summed it and compared with the one on my PC and they were identical. This has me baffled. What am I doing wrong to cause this?