Great answer. To add to your scenario a little, you could imagine also that if there are merchants who accept both shitcoin and hardcoin, consumers might dump their shitcoin there. The tendency to do so would be stronger the more fixed the merchant holds the shitcoin/hardcoin exchange rate. That's where Gresham's Law plays out on the micro scale.

As to whether a better money does drive out the worse money, how would we know it's the better money if it didn't?

In a subjective value framework, the only standard by which something is better money is that people prefer using it to other monies for money stuff, right?