Earlier quoted context omitted.
Then, maybe, use Bitcoins for payment and Tor+HTTPS while signing up for the hosting provider?
Bitcoin transactions are chained, that may compromise you. But you could use an anon currency-exchange or currency-bridge like paysafecard.com to obtain some value and obtain bitcoin with that value and never use that bitcoin key again to avoid that.
If not there should be. You send X amount of bitcoins to a middle man who then gives you X amount back. Technically they will be different coins and they'll go to a different account #, so you can't trace anything.