So as I type this the votes are charging up the ranks (about 10 votes since I started typing this comment), so let me start off:
I can't possibly see how this is Amazon's fault. You're arguing that you offer a service for free (for a little while anyway), and that more people are taking you up on that because they have logs lying around, because Amazon has prompted them in the past to save these logs?
I mean, shouldn't this help your service?
a) now people can try it out because they already have logs and don't have to wait (which you've already identified was an issue), and
b) now people will end up with a bucket full of logs, think 'how can I analyse and use these logs', and go looking for a product like yours!