How to change the successor of a singular with a Woodin? I'm looking for references on how to change the successor of a singular cardinal from "more or less" minimal assumptions. If possible, then without adding bounded subsets to the singular either.
In some papers (Gitik's Namba variant paper, for example) I saw footnotes or mentioning that with a Woodin cardinal you can do this using stationary tower forcing. But I couldn't find any references to a written result.
To make this more concrete, let me put the following question.

Suppose that $\aleph_\omega$ is a strong limit cardinal in $V$, and there is a Woodin cardinal. Is it possible to collapse $\aleph_{\omega+1}^V$ without adding bounded subsets to $\aleph_\omega^V$? (I don't mind some structural damage above the new $\aleph_{\omega+1}$, though.)

(I'm saying "a Woodin", but really I mean "approximately a Woodin", in the sense that there's no issue requiring some measurable, or even a second Woodin, above it.)
Any references, or even a sketch of the proof, would be great.
 A: Assume $GCH$ holds and there exists a proper class of completely Jonsson cardinals and let $\gamma<\lambda$ be regular cardinals. Let $a=\{ \alpha<\lambda: cf(\alpha) =\gamma\},$ and suppose that $a$ belongs to a $\mathbb{P}_{\infty}$ generic $G$ with associated $j:V\to V[G],$ where $\mathbb{P}_{\infty}$ denote the stationary tower class forcing, using arbitrary stationary sets $a$ as conditions.
Then in $V[G],$ the cofinality of $\lambda$ is changed to $\gamma.$ cardinals below $\lambda$ are preserved and if $2^\delta$ is less $\lambda,$
than  then no new subsets of $\delta$  are added. 
so for example we can change the cofinality of $\aleph_{\omega+1}$ to say $\aleph_{10},$ without adding bounded subsets of $\aleph_\omega.$
This is known as generalized Namba forcing. A good reference is Larson's book "The Stationary Tower: Notes on a Course by W. Hugh Woodin". Another nice reference is the notes given by Sy Friedman $\mathbb{P}_{max}$ and the stationary tower.
Note that by core model theory,
such a weird eeffect cannot be achieved if $ZFC$ is preserved by adding $V$ as
an additional predicate, without using more than a Woodin cardinal and
probably this would need a supercompact cardinal.

Suppose that $γ < λ < κ$ are regular cardinals below a Woodin
  cardinal $κ$. Forcing with $\mathbb{P}_{<\kappa}$ below the condition $a= \{α < λ : cof(α) = γ\}$, we
  get that $j[∪b] ∈ j(b)$, i.e., that in $M, j[λ]$ is an ordinal below $j(λ)$ of cofinality
  $j(γ).$ This means that the critical point of $j$ is $λ$, and that $cof(λ) = γ$ in $M$.
Furthermore, if $α$ is such that $2^\alpha<\lambda$, then all subsets of $α$ in $M$ are in $V.$
  Since $V_\kappa^M= V_\kappa^{V[G]}$
   , these facts hold in $V[G]$ also.

See also Larson's notes Six lectures on the stationary tower
.
