They can create their own crypto-currency on top of an existing one, using dogeparty or counterparty. This is most likely their best bet, because they won't fall into a lot of the security/hashrate traps with a lot of new coins.
The fun thing is that as soon as I saw the plans to distribute ownership earlier today, I figured why not use their own cryptocurrency? I guess I'm starting to predict the future, albeit only a few hours in advance