Do you think Dr Polak actually reads the Pali personally? He does have copious Pali quotations, but I get the feel that he's actually relying on English translations. One giveaway was this comment -
On the other hand, in the Pot.t.hapāda Sutta (DN 9), the last stage of the process of meditation is simply described as cessation. But the Pot.t.hapāda Sutta gets into trouble when it attempts to describe this stage of ‘cessation’. According to this sutta, in this stage one finally lays to rest the activity of vitakka and vicāra. It appears that the compiler of the sutta must have forgotten that vitakka and vicāra are gone already in the second jhāna.
I could not trace this anywhere in DN 9. The closest that comes to it is Ven Thanissaro's faulty translation -
(on reaching the attainment of Nothingness)-
Now, when the monk is percipient of himself here, then from there to there, step by step, he touches the peak of perception. As he remains at the peak of perception, the thought occurs to him, 'Thinking is bad for me. Not thinking is better for me. If I were to think and will, this perception of mine would cease, and a grosser perception would appear. What if I were neither to think nor to will?'  So he neither thinks nor wills, and as he is neither thinking nor willing, that perception ceases  and another, grosser perception does not appear. He touches cessation. This, Potthapada, is how there is the alert  step-by step attainment of the ultimate cessation of perception.
The PTS and Walshe translations both correctly translate "imā ca me saññā nirujjheyyuṃ" to mean that "these perceptions of mine would cease" (both imā and nirujjheyyuṃ being in the plural). It looks like Polak was using a faulty English translation of DN 9 to criticise the poor redactor of the Pali!
I don't even know where he found the nouns vitakka and vicāra in DN 9's discussion of ultimate cessation, since that passage discusses the verbs ceteti and abhisaṅkharoti instead.