Lets put a condition for the free distribution.
Every user who applies for free distribution has to send a wallet screen shot with their address and a balance of at least 200 coins.
This will create a small buy pressure and only serious people will apply for the distribution.
This also helps in a way to reward the existing holders, as they dont have to buy any extra to take part in the distribution process.
How about for every 1,000 coins you hold you get 100 free or something like that. That will make people want to buy more to get more free. I'd set a cap on that. Make them pull the coins from exchanges and deposit to a wallet address. Then you can make a program to reward all address with X number of coins based on how many they hold. This of course is just a rough idea. Tweak it if you like it.