Why do you still referring to the block signature? It has nothing to do with forging.
You cannot iterate through many different possibilities for the generation signature because there is only one possibility for each account.
I've looked through the code again and I am wrong. The generator signature is completely deterministic and not a signature just a hash. This allows a forger to look ahead and see likely next values of the generator signature/hash and so simply transfer coins to a public key calculated such that it has a high probability of being a future forger.
Well, it is not that easy, though. You need to wait at least 1441 blocks for a new account being able to forge.
During this period, real-world randomness could easily destroy the ability to forge of your carefully crafted account.
Furthermore, we are going to introduce more entropy in order to predict the next say 20 forgers (which is required to have a high transaction rate) but after that it is completely random.