Yes.
Nancy Pelosi has accumulated too many enemies in a long career to be accepted as President, though she might work out as a temporary care taker.
Hillary Clinton has also accumulated too many enemies in the course of her career. She is a primadonna as bad or worse than Kamala Harris, and is likely viewed as uncontrollable.
The factions want a person who will obey their orders and still put on a credible show as President. Their problem is than none of the convenient choices (Harris, Pelosi, Clinton) really does what they want. How they solve that problem is still not visible.
And, of course there may be no solution to that problem for the oligarchs. They have set far too many forces in motion which they cannot truly control.
You have painted a word picture of a rat cage fight.