Thanks, Joel!
So, my understanding is that if we change any of these
1 then we have to rehash all previous parts of the message (i.e. the block), thus changing the first three words in the share on which a miner is working, and
2 this is what a pool does when all valid values of the nonce have been tried.
Correct? Is there anything other than w[3] (that all kernels are currently changing) that we can change on the client side without having to change w[0] through w[2]?
(Joel - I'll send you a whole 1 BTC when you answer this, even if the answer is a no

thank you very much!)