Just to close the loop on this forum post, we worked through it more offline via email and I discovered a bug in the Download Tool. I made a change to the site to fix the bug this afternoon.
I was pretty dumbstruck when I found it, but it turns out the problem was that tool didn't work for anyone east of the UK because they have a positive GMT timezone offset and "+" is a special character in URLs. Anyway I'm glad to hear it's working for you now!