Tuckmans Ladder: Stakeholder Conflict: Engineering & Procurement Firm

Hello. I am a project engineer at a staffing agency. The project manager and the procurement manager are storming. They were long before I started, 6 months ago. We are in the execute phase of the project with materials and vendor documents being delivered. 

Waterfall projects
Client - Oil and Gas giant
Agent - the company provides engineering and procurement services to the Client.
Company - the vendors whose products the agent buys to ship to a separate construction company.

There is a procurement manager whose team works on all the projects in one portfolio. The procurement manager does not believe that the department is beholden to the project managers. 

The procurement manager is a functional manager, reporting directly to the Portfolio Manager and the Director of Procurement. The procurement manager has setup and agreed to be tracked by key performance indicators which only include required on site dates. Basically if the vendor documents are late or the material is not delivered by the contract date, it doesn't effect procurement departments KPI reporting to the client. The supply chain shortages mean if they were tracked, they would not meet their KPI's on a regular basis.

The procurement manager is resistant to change but has good leadership skills.

The staff of the procurement department have two reports. The procurement department manager and the functional manager (expeditor reports to global manager of expeditor) (buyer reports to global manager of buyers) . 

The project managers have had continuous problems with the procurement delivering vendor documents and materials on schedule. I have been bumped down from being a project engineer to working directly in the procurement department to analyze the situation and report back my findings, which are:

- continued supply chain shortages which would need client to solve.
- lack of professionalism within the procurement domestic staff.
- lack of experience within the procurement international staff. 
- lack of attention to detail from all staff.
- No KPI tracking for items that directly effect engineering department (who makes the company all the money).
- Attitude: Small project mentality, hesitant to take on larger projects.

The project managers report to a Delivery Manager (who reports to the Portfolio Manager). Therefor any "top down" solution must include both the portfolio manager and the delivery manager. Bottom up training is needed to progress the skill set of the group (experienced and inexperienced).

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My primary concern is repairing the rift between  one of the project managers (Tier II project) and procurement manager. The project manager believes that the procurement department is getting paid by the project and should execute procurement in a way where the project can meet it's KPI. The procurement manager believes the procurement department is only beholden directly to the client, and the portfolio manager. The procurement manager believes that in this global corporation that service could be provided to non local projects through the local department.

I am asking for advice and links to any PMI reading resources that would enable me to solve this dilemma. 
My goal is to work myself out of this new job.