Here are a few other ideas for the mix since the lack of movement on the project is clearly surfacing a tension for you.
- Offer a trade - what you can you or another role take off the plate of the project holder to allow it to rise in priority for them.
- Unless there is domain protection keeping you from it, lobby with the roles responsible for the allocation of resources for what the project needs.
- If this is truly a huge project, there may be some ambiguity about next-actions within the project. Can you break it out into sub-projects that are more readily accepted by other roles that align with those pieces or as individual actions by partners with the specific expertise needed.
I hope that helps a little. I can certainly understand the effect on the psyche of having to report "no update" on a project that will repeatedly surface tension.