Surprisingly, this is actually a much more practical solution than what many other people here are proposing.
Sure, if one has money enough to sponsor a trust, then that'll work. But for those with more modest means, storing it on a blockchain is a solid(!) alternative.
The biggest factor here is the choice of the blockchain. One can go with special purpose ones like you suggest, they take care of the details of storing the data, but those blockchains risk losing momentum.
But it would be quite cheap (compared to setting up a trust) to use Bitcoin for this too. Bitcoin isn't meant for this, but there are ways of encoding the website's data and have it be part of the Bitcoin blockchain, spread out over multiple transactions.
The issue there is that the algorithm to deconstruct the data, as simple as it might be, would need to be separately communicated.
A slightly more riskier choice technically superior choice would be to do this on Ethereum, since the exact program for reconstructing the website from the data in the blockchain can also be deployed as a smart contract on the blockchain. So all the great grand children would need to be aware of is the address of the contract, and that it is on the Ethereum main net.
That said, one risk is -- while the specific blockchain might remain, who knows what it'll be called 500 years down the line. So the problem would be, while the website "exists", it's URI might change.
Interesting questions.