"such that the money supply is constant on a per capita basis"

Let's see if we can get the same result using a precious metals-based monetary system with 100% reserve banking:

1. The money supply grows at the same rate than above-ground bullion stocks. Since after Hubbert's Peak the extraction rate of all minerals will decline, the rate of growth of the money supply will be very low, tending to zero.

2. For reasons amply discussed in TOD, population growth will also stop.

Thus, in the Steady-State scenario feasible after PO, a pm-based monetary system with 100% reserve banking would provide for a constant money supply per capita.

See also that deposits in 100% reserve banks not only do not yield interest (as those banks do not lend) but also experience a small demurrage from the fee the banks cover for their service, though that fee might not be proportional to the account balance (e.g. they might charge per transaction).

Now, why do I prefer this system to yours? As I said in other comment, for simplicy and resilience. Frankly, your system (particularly "Newly created money is distributed evenly to every person") is very good indeed, but with human nature as it is, I don't think it stands a chance, particularly for big countries. And sure enough, while your target system could be zero inflation even in negative growth periods, a gold-based system would cause some inflation during those periods (same coins, less goods). A bit of inflation, however, is not seen as bad by Gail and others.

You are also right in that the transition is important, and your steps might be useful also for the transition to a pm-based system.