So............. the OP want a new Bitcoin that would that miners would pump out 950,000 coins every minute = 1,368,000,000 coins a day. And these coins will be sold to bitcoin users who are FORCED to buy them at at least $1 per coin.
I think there's around 100,000 - 200,000 bitcoin users (based on Mt.gox hack last few months revealing 60,000 accounts). Probably, less than half of that is active.
You know what, i'll up that number and give you 1,000,000 bitcoin users, who will be absorbing the coins from your new system. This means each user today will have to spend $1,368 a day to buy the coins popping out from miners. Would you like that? (If they don't buy it, the miners will trade them for $1/coin worth of goods from Bitcoin-accepting merchants anyway)
OK, look, NO ONE would be "forced" to buy any particular amount of coins a day, nor are miners required to sell all coins mined each day (indeed, at these prices they would not need to). If you normally buy $100 worth a BTC a week today, just continue buying $100 of BC2 a week in the new system. The miners would be socking away wealth (in the form of BC2) like crazy, but because of this, more miners will rush in, and so over time, the difficulty will increase until eventually miners are only just breaking even again. But in the meantime, because mining is so lucrative, everyone will be joining the Bitcoin network to mine (hey, free money!) and signing the contract, and so acceptance will skyrocket, and approach 100% very quickly. Soon, everyone will be accepting BC2s.