Sorry for my tardy response to this thread, but I done been busy.
When Bellow refers to the heart's ultimate need, what is he referring to, exactly
Christ knows what Bellow was thinking, but here's my interpretation.
The last scene is a funeral, in fact, I first read it as literally Wilhelm's own funeral due to the abrupt end of his thought whilst he's rushing madly in the busy street. This line of thought led me to read the end of the book in terms of who the corpse meant to represent to Wilhelm.
I think that the corpse is representative for Wilhelm of both himself and his father (the corpse is described as a sort of cross between father and son) and that this view gives a possible answer to Micheal's question.
On the final page of the book, a bystander at the funeral, who could be talking about the likeness of the corpse and the corpse's brother or the corpse and Wilhelm, says,
'They're not alike at all. Night and Day.'
The ambiguity of who the bystander is talking about can be transposed to the corpse that, in my interpretation, represents both Wilhelm and his father.
That is to say that the new Wilhelm (post epiphany) has freed himself from, and therefore is different to, the old Wilhelm (as represented by the corpse) and, more importantly, that Wilhelm is nothing like his father (also represented by the corpse).
In relation to the question Micheal asked, this interpretation may stand or fall on what it is that Wilhelm hears that leads to the 'consummation of his hearts ultimate need'.
The line, 'He heard it.' is immediately after there is music, however, the last line of dialogue he would've heard is ...
'They're not alike at all. Night and Day.'
So, in my interpretation, his hearts ultimate need is to be declared different from his father.
Here the view that the corpse is representative of both Wilhelm's old self and his father works on the two levels that only need a singular 'ultimate need.'
Throughout the story (although he often protests it) Wilhelm is like his father in many ways and therefore the old father-like Wilhelm corpse can be seen as being different from the new (epiphany improved Wilhelm) just as he can enjoy being seen as different as 'night and day' from his father when you see the corpse as his old man.
I think my thinking in this may also have been swayed by reading Bellow's,
The Dangling Man, in which the protagonist comes across a picture of his grandfather and knows that as he ages the old man will reclaim his face.
So I think that Bellow has a bit of a theme about the impossibility/possibility of escaping the awfulness of your antecedents and that this not only means your parents but the actions of humanity past as well.
Having said that, and pretty badly (I hope it made sense), I also see Milly and Micheal's interpretations as valid and would add that it his 'ultimate need' could be the death of his father or, more simply, to be loved.