Mission completed - I finished downloading all the PDFs (at least one version of each PDF in the Humble Bundle).
Thanks and kudos to the tech team who managed to stabilize the situation.
Two things helped me in the end:
- Internet Explorer instead of Chrome. I never expected to say that in my life :(
- I personalized in batches around 5-7 files, then I went to do something else (showering, eating, household, ...). When I came back 15-30 min later, I could download the batch, then personalize the next.