I don't think we can know exactly what will happen with this setup without the actual stable coins in existence. My guess is, the higher transaction fees would cause people to hoard the coins. This will then remove more coins from existence than the higher transaction fees, and thus cause the price to rise.
Anyone desperate enough to sell below the fair value, would also likely be desperate enough to pay the transaction fee. Hoarders would then have an opportunity to make money through arbitrage, and coins would be destroyed at the same time.
In other words, I think the threat of higher fees or higher mining rewards would keep the price fairly stable without the actual higher fees or higher mining rewards going into effect that often.
I will be so, so happy when this hypothesis actually gets tested by someone

The problem with a distributed exchange is, there is no central authority to enforce trading fees. Otherwise, it would be a good idea.
Dang. You are right. I don't know why I didn't see that - even if everyone somehow used the same rules on the distributed exchange, people would just trade outside of the distributed exchange.
I'm increasingly convinced that you have the right approach here. I'm just worried about the coin destruction driving down coin prices rather than driving them up. If you can handle the "doomsday scenario" where 90% of people holding these coins panic that the coins won't hold their value, I'll be totally convinced.
People don't behave rationally during a panic, and I don't think you can rule one out.