Truly paranoids are/will/should use Bitcoin or Litecoin. I don't get why pricing is USD$ only, it just seems that cryptocurrencies are perfect for this kind of service.
As others have said, this depends on your definition of paranoia. If you're paranoid right here and right now, you can always go to your local 7-11/Walgreens/etc and get a prepaid credit card to pay for this.
If your opponent uses geographic profiling, you want to pick a point far away from you and then go to stores far away from that point -- then they'll identify that far-away point as being your origin. If your opponent is a game theoretician, on the other hand, you want to pick stores to visit completely at random, in order to avoid providing any information.
Perfectly serious snarkless question - how would that work, financially? You're reselling S3 storage with your value-added service on top - obviously you set your prices in a way that pays for your costs, time and generates some sort of profit. Short of adjusting your prices on a daily (or hourly!) basis, how would you be able to accept payment in a currency of such extreme volatility?
This is why I don't accept BTC yet -- unless the exchange rate settles down I'm only going to be able to do it via a service which lets me say "I want X USD; make it happen".
Coinbase comes close -- the only thing they don't do is allow me to specify at run-time how many USD I want; for some odd reason they need you to "create a button" with an API call before displaying that button on your site, which is a pain to deal with when you have variable payment amounts.
Why not add a simple public page to the Tarsnap website that allows the visitor to gift x dollars to the foo@example.com account? That way, bitcoiners can use bitspend.net etc. as a proxy payment provider for the time being.
Not leaking metadata on credit card statements that allows to infer that valuable data is stored at Tarsnap (and approximately how much), would be a practical increase in security: Such a leak might prompt an attacker to allocate more resources towards compromising the Tarsnap user's client computer.
I'm guessing it suggests that those who are truly paranoid about others snooping into their tarsnap-saved data may want to make their tarsnap payments anonymously as well.