It sounds like the main problem is that you're dissatisfied with the organization's bureaucratic, documentation-heavy process; you've worked elsewhere where talking face-to-face and actually working on stuff gets things done faster than writing and passing around Big Documents (which often don't get read).
Trying to convince a company or a project team that has an entrenched "waterfall" mentality to even consider some iterative and agile ideas is difficult (I've tried).
So maybe start small: Try proposing a Lean Documentation or Agile Documentation strategy for your internal UX materials. The goal is not to "eliminate" documentation -- obviously there are things that really do need to be written down -- but to cut down the number of documents and to simplify them:
- Try to focus on recording only what your audience really needs;
- Use documentation tools that encourage iterative editing and collaboration;
- Do away with elaborate formatting;
- Use the written word only when appropriate (e.g., retaining specific details for the long term, recording design rationale for future reference, or explaining something complex to many people); where possible use diagrams, illustrations, interactive things like what-if spreadsheets, etc. And some things can be communicated perfectly well face-to-face, on the phone, or in a presentation.
For example, rather than writing up a formal usability test report, suggest instead that you sit down with the designers and developers to explain the problems you've found, and then write down and keep track of those issues to be corrected using a defect tracker like Bugzilla. (This also makes it easier to track what has been fixed.) Keep your problem descriptions short and illustrate them with screenshots.
Consider introducing a wiki, if your company or team doesn't have one. In my experience it's pretty hard to motivate people in a corporate environment to actively contribute to a wiki, but if you put all of your UX material there (and only there), team members will have to check it out, and then they'll probably love the ease of editing and collaboration.
I very much like the suggestion of using cartoons and illustrations to keep things short. A 200-page text-only document surely won't get read but a 30-page document full of pictures might... and maybe what your target audience really needs isn't a document at all but something else, like a high-fidelity prototype.
(By the way, this answer is too long to be a good example of Lean Documentation.)