Very clean design!
With the average implied basefee payment (or likely any basefee determination rule that depends on the number of transactions included in the block) there is a non-trivial optimisation problem for the miner to solve due to the interaction between the transaction tip = min(premium, fee cap - basefee) and the transaction fee cap. For instance, a high premium but low fee cap transaction may become less valuable to include in a larger block (with higher implied basefee), vs a low premium but high fee cap transaction. This was already noted to figure out how the transaction pool should be reordered and accessed under EIP-1559. There are likely good heuristics around this issue, in fact likely the same ones that transaction pools will use.
With initial simulations based on the abm1559 library it does seem to be the case that oscillations are not as pronounced with the AMM design vs the classic 1559 update rule (see this notebook for early results).