In this thread we have discussed multiple variants of Seigniorage Shares using an Uniswap like pool as an oracle:
The main problem with adjusting the price of the pool by minting or burning stablecoins is that the liquidity providers lose money when there is a contraction and stablecoins are burned. They will therefore leave when a contraction is expected, emptying the pool. To solve this we could restrict leaving the pool in some way (timeslot, fees etc).
An other way is to make the contract own the pool. For the contract to acquire the USDC collateral, it could sell the Seigniorage Shares. These shares will then collect stablecoins, whenever the stablecoin is undervalued.