You say that refusing to bail out the banks would push a recession into a depression. No. It is the way that the economy has developed over the preceding period that is going to cost us. As I think you acknowledged, one of the weaknesses is that the financial sector has grown too large, while manufacturing has shrunk. Boosting the already bloated banks seems foolish to me, a recipe for perpetuating business practices that took boom for granted, imagining that someone would always appear on hand to bail you out. Better to use their difficulties to force some restructuring.
Your thinking, I think is that boosting the banks is the best way to put some liquidity into the economy. But I fear that we are past that point, and that whatever cash goes in just will not come out again, but only be used to manage their debts. Maybe the US banks are in a better way than the British ones, but proportionately, the absolute debt must be phenomenal there.
I think it was Keynes, not Hayek who introduced us to the idea of deficit spending, when he suggests that the treasury boost the economy by burying money in bottles so that entrepreneurs can dig them up. I think the argument was supposed to be reductio ad absurdem, though you seem to have taken it literally. He does say in passing that it would be even better if the money was spent on some useful public works, which is, I suggest his real meaning.
Deficit spending shoring up the banking sector will most definitely not avoid any downturn . Deficit spending could indeed help to restructure the economy in a way that would at least shorten the impact of the downturn. But that would mean using government spending to direct economic growth in strategically advantageous ways (I believe the incoming president favours green energy, which I do not, but at least he is thinking about the problem). Throwing money at the banks in the hope that everything will go back to the way it was underestimates the dynamic character of economic change. The growth of financial services was scleirotic, there has to be some contraction.
And lastly, you seem very irritated at the idea that NYC should be accused of living on government largesse. I don't challenge your argument that red states are in deficit to blue ones. But if you want to accuse the red states of latching on the government tit, that does not make the argument for directing a trillion dollars your way. Does it go to the hardworking poor of Bed. Stuy.? Of course it doesn't, but then nor do the rewards of government boondoggles in Alaska get distributed on communist principles.