I think the point here is that, BEFORE the community (not just the Token House, but also the Citizen House I hope) should have the power to make this decision, there should be a clear educational path for the community to take on this critical task.
This vote would be only for signaling. So it doesnt matter how the parameters are changed, whether it is a token house vote or a multisig that can just change at will, the community can work together to understand and then design the gas fee calculation.
In short I don’t see the lack of an onchain function to modify the gas params as a blocker for creating a dashboard and a process for the community to make an informed decision to change the gas params, if that change takes time to implement, then it takes time to implement.