There are of course other ways. You could create a facebook page called JINN, you could accept likes and they must become your friend, you would make your friends list open to the public and you would try to look at each Facebook profile to see if it was a sockpuppet. There are varying different ways to do this. For instance if you have 500 out of your 1000 are accounts from Nigeria, then you can know they are sock puppets. There are much more complex methods of sock-puppet removal too via Facebook. You could set the requirements quite high for Facebook activity. Because again, that proved that people made those worked to make those accounts, and furthermore you can profile each account.
Facebook? Really? What is that Proof-of-NSA? lol
A lot of people don't have social media accounts for a variety of reason. Some people would get their non-tech savvy friends to participate in the distribution and then buy their stake from them for $20. You are just giving the illusion of removing "sockpuppets".
You could use the BTT method I suggested.
The point is cryptographic proof doesn't solve the real problem. The real reason you want a wide distribution is to say it was "fair" and not gamed by 20 or fewer whales. Just giving cryptographic proof via MS doesn't do much for you there. You open up your MS to the world to mine JINN and you will have 20 people with 90%. You might as well just ask people to send you a bitcoin for a share of the new project.
You will never get a system that provides you with verifiable "equal distribution", which is what you really mean when you say "fair distribution". Any system that initially provides "equal distribution" will quickly turn into an unequal system. That is life. There is a hierarchy to nature called survival of the fittest and nobody can escape it. I agree that everything should be "fair" but it is impossible to make everything "equal" because people are not "equal". It seems these false arguments always come up around CfB and NXT's initial distribution because people feel like they missed out. I think a very good argument can be made that NXT's initial distribution was extremely fair. It lasted around two months and it did not require users to outlay a substantial amount of BTC to participate, meaning it did not discriminate against the poor. A lot of people didn't donate because they weren't interested or didn't see the potential. That was their choice. Everyone in life makes calculated choices based on their abilities and rational deduction skills and we all must live with our decisions.