“The question is how make the issuance of and access to money egalitarian on the one hand.”
What about work? What about merit? What about talent? Sorry, but issuance and access to money shall never be egalitarian. No way!
They will then complain that the system isn't fair as some who saved, stole or somehow acquired coins would be rich in the new world, just as they are under the current system.
The G.E. government certifies coins as "Great Empire Coin (GEC)" through a network that allows one to spend more coins than they hold. This is the G.E. government's equivalent of empowering a central bank to purchase more bonds than the bank's preexisting cash holdings would permit.
What system is in place to prevent individuals from issuing/spending more money than they earn (in the past or future?)