I don't have a great answer for this problem, but...
If someone wanted to sell 100 Stablecoin this way, they would have to create a new wallet and put 100 Stablecoin in it. If they did this while the price of Stablecoin is low, then they would have to pay the higher transaction fee. Thus solving the problem in this case. If they moved the coin while the price was high, they wouldn't have to pay the transaction fee, but they could just sell the coin for a profit instead. The only way this would work is if they bought the coin when the price is low, then moved the coin into separate wallets when the price is high, then sold the wallets when the price is low again. Not only is this complicated and risky, but the initial purchase would pay the high transaction fee.
An alternative to the above is if someone bought a bunch of Stablecoin at some point and doesn't care about selling exactly 100 coins. They could sell their entire wallet at once with some random number of coins inside. The problem with that is, the receiver couldn't pull the coins out of the wallet without paying the high transaction fees. The receiver would have an incentive to hold the wallet until the prices come back up. He could then sell the coins at a profit and may not have to worry about the transaction fee. Again this encourages hoarding which would drive the price of Stablecoin back up.
The big issue is an exchange like Mt Gox. If there were an exchange like Mt Gox which held all of its Stablecoin in a wallet and let people buy and sell on its open market, then the price of Stablecoin would be independent of transaction fees. Of course, anyone who bought a bunch of Stablecoin while the price is low would not be able to pull it out of the market without paying the transaction fee. This again would encourage hoarding which would drive price back up to the fair market value.
There may be issues in practice, and the transaction fee/miner reward may have to be adjusted at times. I still think it could work and I'm slowly working on an implementation.
If anyone has any info on creating your own bitcoin chain, let me know. I'm looking for a tutorial if one exists. Or maybe a tutorial could be added to the bitcoin wiki.
I'm especially worried about the scenario where somebody writes a client which stores your coins in hundreds of little wallets, and sends and receives wallets instead of coins, completely bypassing the transaction fees and coin destruction. If everybody switched to that method, including the exchanges, then no coins would ever be transferred through the protocol, nor would they ever be destroyed. And people would definitely have a big incentive to move in that direction, even if it didn't get that extreme.