Not exactly what you are looking for but Sidebery has a feature called Snapshots that allow you to save a group of tabs in their current state to open them later.
To be honest, I think the only "piracy/privacy friendly" alternative would be to use a stolen credit card haha (I don't recommend it at all and it's a joke).
I think in general all these services will ask you for a credit card in one way or another, and that's fine, they need to make sure that no one abuses their services. The closest thing to something "piracy friendly" you can do is to use an old laptop or computer and use it exclusively for that or even better in a virtual machine.
That's a good point that I forgot to mention, in File Centipede you can't import .dlc files, an incredibly cool feature of JD2 that honestly is a disadvantage against those sites that split their downloads between different .zip files and it's a pain to open each link and download it manually and even more when they are up to 500 links of 500mbs.
I thought that too and it is not quite clear on their page, but it seems to me that the developer means that purchases will be refunded only if you want to once the project reaches 100k on Github. In my opinion sincerely if I donate today I doubt that the day the project reaches 100k I would ask for a refund, and anyway I would never ask for a refund if I want to support its development.
Maybe you can tell developer on his Github of the site where you couldn't download the video, he usually answer.