We have a reoccurring conflict with one of our larger and strategically important customers. 
The company (let's call them "C" for now) sells and distributes technical articles, everything from hardware components to hairdryers, and has more than 400000 products in their catalog.

The product owner, who is also the head of product documentation and internal software at "C", has at some point in the 90's taken a course in software testing, and is now writing "Requirement specifications" as user tests. These are often contradictory and error prone, but she maintains that what she writes is what she want's, until she writes something else (in same imperative but ambiguous and abstract format). Furthermore, she demands a final budget for the project, and is unwilling to work in smaller iterations of budgeting. 

I'm looking for hints on how to control the development-process (and our own economy) and still provide the customer with a product that gives the company most value-for-money.
Normally, I'd start a project by identifying goals of the project and business use-cases of the organization - and then deriving scope from those goals, using User-stories. The details (specifications) of how user-stories should be implemented, is decided at specifications prior to the sprint including the respective user-stories. This has repeatedly proven to result in better products and greater ROI for the customers.

Does anyone have experience of knowledge of techniques that can be used to "Reverse engineer" imperative user-tests, or any other input on how to handle the situation? 

Historically, she has been allowed to completely dominate the development process, which has blown our budgets and taught her that she is in control of our process. Our management has now asked me to control (and defend) the development process. They told "C" that there will be used no more hours than the agreed budget, regardless of how "done" she (the product owner) feels that we are, which of course will be my leverage. She will become defensive, even aggressive to get things her way - any sound arguments based on professional reference or experience would be of help.

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Follow up:

I thought I'd follow up in case anyone stumbled across this post with similar problems:

We have turned the communication around, and are expecting to deliver the next project within budget and on time (I'll edit this post again if hell breaks loose later on).

Initially, I focused on creating trust between me and the Product Owner. That meant choosing the relevant battles, and presenting myself as her tool to get most value for her money. Requirements are still expressed in more or less the same way (although she is open for input about syntax, she is firm about the format: Word Documents and Emails), but we are slowly trading control with visibility regarding the development process. 

I managed to persuade her to participate in weekly meetings for project status, backlog grooming and prioritization. Between each meeting, she gets the chance to test the newest revision, which makes her test-feedback what used to be an object for discussion, the most valuable feedback for the backlog grooming and prioritization. By having a head-to-head talk about the feedback from the tests, we're able to "weed out" misunderstandings, contradictions and scope creep before it leaks into development.

The trust between us enabled us to have a constructive talk about each others organizations and the processes and intentions of these, which opened my eyes to quite a big part of the problems being our lack of capacity (professionally, theoretically, and methodically). 

The product owner has called management to personally compliment the progress we are making, so I'm calling success on these first steps - but constantly watching the scope and progress, as to not "rest on ones laurels"