Sauron - Physical form in The War of the Ring or not?

[Zigûr]

Sauron was never an Eye. I think Letter 246 and Gollum's remark put this beyond doubt. From the end of the Second Age onwards, when incarnate, he looked like an unnaturally large man with burning skin and nine fingers. The Eye was his symbol and how his psychic presence was perceived by those who encountered him in or through the unseen world or how its manifestation was interpreted by those who observed his power (see the flash from the summit of Barad-dûr witnessed by Sam in Mordor).

Sauron did not act through agents and emissaries like the Mouth of Sauron and the Nazgûl because he was some giant telepathic eye but rather because there was absolutely no need for him to ever put himself into personal danger by confronting his enemies directly. His (staged) abandonment of Dol Guldur is testament to this. By the Third Age it had become a time consuming and demanding process for Sauron to become incarnate: he had had to do so quickly after his old body was lost in Númenor, and now he had to do so again.

The Ainur could become incarnate however they pleased (Yavanna as a tree, for instance) but I don't think it at any stage behooved Sauron's interests to become incarnate as an isolated body part - he could not have worn his own ring had he recovered it, for starters. We know that he could no longer assume a fair and pleasing form; is it possible that, like Morgoth before him, his 'Dark Lord' body was now the only form he could take?