I don't think that the noise is excessive, it is only really noticeable at 100% which is pixel peeping and to be honest the highlights are not that heavily blown at regular print sizes it will be fine. The noise is only just visible in relativel constant areas of grey tone, which is caused by atmospheric haze.
I am prepared to be corrected by others, but something seems amiss, but I am not sure that the polariser wil cause it.