If we switched from our current fractional reserve system to a full reserve system, then we'd increase our current seigniorage profits by a factor of roughly ten which should get us to the amount that you mention. Note that we already use the existing seigniorage profits to subsidize the government, so you'll have to offset those in the budget if you repurpose them. You also need to figure out a way to fund banks, as they reap the other 90% of seigniorage profits now.
Banks would also lose loan revenue under a full reserve system. Currently they take in demand deposits (checking, savings) to offset their long term loan balances. Under a full reserve system, they could no longer do that. Long term loan balances would need to be balanced with long term deposits. That would lose banks all the interest that they earn on demand deposits as well as the seigniorage benefits of money creation.
Some have proposed that full reserve banks should charge people to hold their checking accounts (rather than paying interest). A per transaction fee would be used to support banking activities. The credit card system already includes this, charging those who receive money. A monthly subscription fee is also a possibility.
Under a full reserve system, increasing the money supply gives seigniorage profits. The normal use of this would be the same as it is now, the purchase of government debt. This is what is called open market operations. The Fed buys government bonds on the open market. You could purchase other things with it, but so long as government debt is plentiful, this is probably the least disruptive.
It would be possible to switch from open market operations to other kinds of ways to get money into the hands of consumers. For example, they could fund a basic income with it. The problem with that is that the money supply doesn't always increase in size. It usually does but not always. So sometimes there'd be no income. In fact, the government would have to keep some money back to cover shortages, which gets us back to open market operations.
We could get in a situation where we couldn't engage in open market operations. We could pay off the debt. Then we'd no longer have government bonds to buy. We'd have to come up with something else to do with the money. Funding a basic income is a possible solution.
It's unclear to me what could cause us to balance the budget and pay off the debt in a short time (one to two decades). Perhaps government funded research discovered a revolutionary new, non-polluting energy source. The initial rush pays off the debt and the ongoing royalties pay for the government budget. Income taxes are canceled. Not sure if that fits your story or not.
Or we finally make robots that can build themselves. The accompanying revolution in labor causes an increase in production but leaves many unemployed. Thus we need both a way to get money to the newly unemployed and have more tax revenue from the increased production. Again, not sure if that fits your story.
If neither of those fit, you may want to ask another question where you can better describe what would fit your story in terms of causing a balanced budget.
Possible Premise: A law is passed saying that the sale of bonds on the open market (increase money supply/increase inflation) results in unequal distribution.
Note that this is backwards. The sale of bonds by the Fed decreases the money supply and therefore inflation. It's the purchase of bonds that increases the money supply and inflation. That's not to say that a law couldn't be passed saying that, just that the statement would be incorrect.
In this situation, I'm trying to re-invent the monetary policy as it would apply to virtual currency, as different distributive mechanisms are available. Discount windows would have a different implementation since I'm creating a run-free financial market.
Actually there aren't different distributive mechanisms available. Part of the confusion is that we already have a virtual currency. The only thing is that our current virtual currency is completely interchangeable with our physical currency. So I can deposit virtual currency in my bank, transfer it to PayPal virtually, and then transfer it to your PayPal account virtually. You can then transfer it to your bank account and get physical money (bills and coins).
Switching to a purely virtual currency doesn't give you more options. It gives you fewer options. In particular, you would no longer be able to get, hold, or spend physical money.
Some of what you note as benefits of a virtual currency are actually benefits of a full reserve currency. Perhaps your vision of virtual currencies is influenced by those who believe that they should be full reserve currencies. Thus, you are attributing benefits to the virtualness of the currency that should be attributed to its reserve rate.
An increase of the supply of money means that they want the value of money to decrease respect the goods it can be bought. In other words, the goods will be worth more money. In other words, the objective is to increase inflation. While it is a rational objective (to avoid a situation of deflation), the usual tool is lowering interest rates (so banks, business and people have more incentive to get loans).
Actually, the usual reason to increase the money supply is to keep up with the expanding economy. Inflation results because we prefer to miss high rather than low. Missing low causes economic growth to slow, possibly causing the economy to shrink in extreme cases.
It's common to say that we increase the money supply by lowering interest rates, but really, the reverse is true. The way that we lower interest rates is via open market operations. In this case, the purchase of government bonds. This pushes cash into the banking system (increasing the money supply), which causes fewer banks to need loans to cover their reserve requirements and more banks to have money to loan. Fewer banks requesting loans and more banks offering leads interest rates to fall.
This is why the main number that the Fed sets is called the federal funds rate target. The federal funds rate is the weighted average of all interbank loan interest rates. The Fed sets a target for what that number should be and engages in open market operations so as to hit that target.
There's also a theoretical argument that lower interest rates cause increased borrowing. In theory, people might find a loan worth it at one rate but not a higher rate. However, this doesn't hold up in practice, as interest rates are set by the market. If banks had extra money to loan, interest rates would fall. Again, the money supply determines the interest rate, not vice versa.
Another theory is that when there is more money to loan, that banks respond by decreasing their loan standards. Banks make riskier loans when money is plentiful. They do this because interest rates are generally already low enough that it makes economic sense to borrow.