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.