Unilateral amendment might be a bit of a misnomer because its basically a new contract that your continued use implicitly accepts. There is never any retroactive term change. If they unilaterally change the notice period to 12 months and you reject, you would have to give your of rejection but it would be under the 6 month term because you are not accepting the new contract.

Unless there are other provisions for unilateral changes for contracts in the termination period, no new terms would apply to your final 6 months.