Model the central banker as a three color channel

The central banker has the power f government and is the dominant player.  That is why the seigniorage fee must be a bettable process.  The deal system has that calculated, it is not. The seigniorage fee should be driven to a stable, almost always repeatable ratio, like a fixed ATM fee.

That is the problem, right there. The non market seigniorage fee causes unseen forces on the liquidity markets. That fee is used by Treasury to cover liquidity short falls, which is fine, it can collect its fee. But Treasury needs to find its own causes of liquidity short falls. We need to bet Treasury blunders ex ante, and improve our bets ex post.  Acknowledge typical losses by the government sectors.

Pay the seigniorage fee in longer term contracts, allowing us to internally do set asides for it. We are moving spectrum, we are adding a long term axis on which to measure short term variations. Like NGDP bets. Making a new yardstick. We get deposits, loans, seigniorage; triple entry accounting.

Government can demand it, up to the limit, then a new contract is due.   But the transaction costs of renegotiations are unpleasant for both sides, they tend to be honest about government's expected losses going forward. But without a default reserve,  Treasury and Congress are in a bit of hurt, these default contracts are a bit of  liquidity blessing for Congress. We can get a fair trade on this.

Congress sees it, and can turn a stable seigniorage rate into cash, via the Fed executing this optimum random seigniorage contract over the longer period. Force Congress to seek gains by 15 year, accurate planning. The seigniorage income becomes earned, payable to state capitals evenly. The seigniorage contrac tbecomes a trade between the House and Senate, the axis is maintained at the root cause. Quantizing the side lobes, making quarks, jumping up the Markov tree. The system will always seek to lower the Markov rank back to ground state, and eventually we may just pay a standard  monetary fee, transaction costs measurably zero, two color.. It is all ultimately micro.

My guess is that the fee should be about a quarter to half point of flow, in stable form it appears like a semi-repeaatble loss by a two color pit boss.  ATM fee goes up from a point to a point and a third. Maybe a hundred fifty  billion/yr, half of that earned cash to state capitals.  Earned meaning their senators do a good job.