Your dumb fucking idea relates to finding the key to 1 specific address. I am looking for the key to any of millions addresses that have bitcoin stored on them. So, my problem is much, much, much easier than your stupid problem.
Wrong. The 'fastest' method would be a birthday attack, and you still need O(n/2) operations (i.e. 2^128 operations for SHA256 if you had enough memory). Just because you aren't looking for a specific key to collide with, that doesn't really make it likely to find a collision in this case.
Nope. 300 million seems like a lot until you realize billions, trillions, quadrillions, octodecillions are nothing compared to the probability of a collision.
Let's add some numbers in here:
In order to spend money sent to a Bitcoin address, you just need to find a ECDSA public key that hashes to the same 160-bit value. That will take, on average, 2^160 key generations.
Supposing you could generate a billion (2^30) per second, you need 2^130 seconds.
Doing this in parallel using a billion machines requires only 2^100 seconds.
Getting a billion of your richest friends to join you gets it down to only 2^70 seconds.
There are about 2^25 seconds per year, so you need 2^45 years.
The age of the Universe is about 2^34 years so far better get cracking!
Source.