Hi Matthew,
Thank you for your support for APT and apologies for the inconvenience!
I have sent you a workaround link which should do the work. Also, in the APT site when you enter your key/email and click on Download you will see alternative download link.
We know that in less than 1% of the downloads is possible to have problems. A lot of hours have been spent trying to fix that, however it is not possible to reproduce it in a development environment

We have tried to apply every hint posted in the net, but still sometimes there are broken downloads

It is something related to the client connection, not the speed, but possibly dynamic routing made from the provider or something.
As for the PayPal process, it is completely out of our hands. PayPal has their security policy and does the versification. We just sent a link in order to identify that there is a request for payment. Once you click on the button in our site, everything is done by PayPal itself.