It seems pointless to consider developing a stablecoin based on Bitcoin. We already have a system like this called Satoshi, where 1 Bitcoin is equivalent to 100,000,000 Satoshi. Satoshi has been supplying stability and transactional convenience within the Bitcoin network, playing a function fairly similar to your conception of Bitcash.
Additionally, the stablecoin is linked to Bitcoin, which is not stable. The volatility of bitcoin is both what attracts investors and makes it a lucrative asset, as well as what makes it a difficult stablecoin option. This claim sounds less like a workable financial answer and more like an intellectual exercise.
And if that is the case then why bother ourselves trying to make bitcoin stable or to create some sort of stable coin out of it, when the volatility that we see on the bitcoin market plays on our favor.