I have not yet received an answer to my own question thread
(which would allow me to answer with more certainty). However, I think I have a bit of a grasp on how it works. Just take what I say with the appropriate grain of salt.
The contents of the block that you are trying to hash (below the target difficulty) is constantly changing, with every new transaction and/or block that is validated. So even under the (highly unlikely, I think) possibility that some static block text does *not* have any hash value that would match the current difficulty, your miner will update it with the current information as it comes in through the peer network.
So it is not possible to get "stuck" forever. It is, however, highly possible for you to never (or not for a long time, at least) be the lucky one to find a current hash and get it published before someone else does.
Regarding your second question, there is likely to be a *lot* of redundancy across the entire BitCoin network, given the nature of brute forcing hashes. Although I would expect that mining pool servers try to minimize redundancy within their own pool.
I'm not quite sure what format BitCoin uses for its timestamps, but most computers use milliseconds (since the Unix epoch) rather than seconds. Either way, I don't think this matters. Even if a given mining pool some day has the computational resources to calculate all possible nonce hashes (which would be practically guaranteed to find a hit), everything suddenly changes as soon as the pool server receives a publication of a new block or transaction.