You have your head on straight.
Though I have to disagree with your take on the Greenbacks. Not because they weren't a good idea, but because the government mismanaged them. By the end of the civil war they were only worth 33¢ against Gold Dollars (1/60th oz of gold, vs 1/20th oz of gold for the dollar.)
It is not possible to increase the actual size of the economy by printing more money.
Here's a way to look at it that should make some sense.
Let's say you have a company called XYZ Company. Now this company has issued 100 Million shares at $1 a share, and the market price for those shares has remained at that $1. The value of XYZ Company is going to be $100,000,000.
Now, if you announce a stock split of 2 shares for every 1 share, you are going to have 200 Million shares, but each share is only going to be worth 50¢/share leaving your market valuation at $100,000,000.
Of course, now you have 200,000,000 shares.
It's much the same way with dollars. In 1913 Dollars we have an economy that's worth $600,000,000,000 However, since 1913 we have seen the equivalent of stock splits that total 22:1. Now, since the value of the economy in 1913 dollars is only $600,000,000,000 and each share is worth $1, when the shares are increased by 22 fold you end up with 13.2 Trillion Shares (Fiat Dollars) which still only have a relative value of $600 Billion.
There was no value created by this measure.
Now, if there are people that get paid $5,000/year in these fiat dollars and their pay doesn't go up with the split then you see their actual pay go down.
For instance, if Joe the Plumber was making $5,000/year and saw that only go up 800% he'd only be making $40,000. Since he was shorted 1,400% however, his new pay is only worth $2,857 leading him to actually be worst off by the equivalent of $2,143, despite seeing is income jump $35,000/year.
That's why inflation is bad.
Of course, luckily for most citizens their pay has done a reasonable job of pacing inflation, but it still has fallen behind leading every American to be ultimately poorer.
(2200% is the total inflation from 1913 - 2007)