Elizabeth asked Rose to write 30(!) pages of literature review -- a "rough draft" -- which Elizabeth will use to write her literature review.
Let us all acknowledge the elephant in the room. No, there is no ethical way to handle this, as Elizabeth does not want to handle this ethically. It seems painfully obvious to me that Elizabeth is outsourcing the writing of her dissertation, or at least parts of it, under a thin veil of "help" and "drafting". Given that Elizabeth is giving Rose clear length instructions and everything, I would be surprised if "draft" in this context is anything else than an euphemism for "please write this for me, and I will do some cosmetic changes and hand it in".
Any of the proposed solutions (publishing the material beforehand, claiming authorship of this chapter, ...) will not be accepted by Elizabeth, as it will not accomplish the goal she is rather evidently going for, which is getting her literature review without having to actually write it. Besides, it seems extremely dubious to me that any serious thesis committee will allow some of the proposed solutions (e.g., explicitly having a different author for chapters of a thesis - the reaction of any committee in any university I attended would be between bewilderment and anger if you proposed that).
As such, there are only two ways forward for Rose:
- Tell Rose friendly but in no uncertain terms that she cannot do this. She can get a little creative with the reason if she does not want to tell Elizabeth that she finds the proposal unethical, if she must.
- Go forward with writing the literature review, but be aware that she is actively involved in a case of academic misconduct, and that there really isn't a way to rationalize this differently.