Is there any strong opposition to moving to a faster blockchain?
Would Dogecoin be the best blockchain?
On a related note, this might not completely solve the issue, as it seems that the NY Lottery numbers have been slightly delayed recently, which also contributes to the slowness, so we may still have to consider other sources of randomness.
What about PoS cryptos, like NXT or BlackCoin? Both of them feature very fast confirmation times.
As per randomness source, I recall there was a discussion about Cha origin in some place (where NY was criticized as possible, albeit unlikely, to be manipulated), and some natural sources of randomness like seismic activity were suggested.