It's an interesting thing to think about, and you're actually correct in your points, but unfortunately you're not considering magnitude.
First, yes, it is very reasonable to conclude that lowering the minimum wage or eliminating it would result in more employment. However, eliminating a price floor only makes a difference in markets where it was binding - eliminating a $7.25/hr min wage can only affect markets in which the equilibrium price would have actually been below that number. How many labor markets in the U.S. do you think that holds for? Not many. Teenagers and very unskilled individuals.
So, let's say you do eliminate the minimum wage. Clearly, people will not work for a given wage if it is not enough to live in some area around the job. You seem to answer this by saying that price levels will drop. It's tough to make conclusions just "eye-balling" the economy like this, but that's probably true as well. But by how much? It is only reasonable to conclude that, 1) prices will drop in the market for products and/or services produced by those now paid under $7.25, and 2) prices will only drop substantially if the cost of bringing the good/service to market was largely dependent on the cost of labor.
So basically, the price level couldn't drop that much. Even in the absence of the min-wage, manufacturing won't move back in great numbers...unless U.S. workers will work for a few dollars a day, which won't be possible because given the current price level such people would starve.
So it's an interesting point, but it's NOT really the problem we face right now as a nation. The vast majority of us, unemployed or not at the moment, would not be affected by a min wage decrease.