Would a Project Management degree help me move into a Tier 1 infrastructure role, given my experience?

I’m considering completing a degree in Project Management to improve my chances of moving into a Project Manager role with a Tier 1 infrastructure contractor.

I currently work as a Project Manager for a structural steel engineering and fabrication company. I am in my early 40s :( My experience includes design coordination, shop drawings, procurement, fabrication, QA, programming, subcontractor coordination, installation, variations and overall project delivery.

While I haven’t been directly employed by a Tier 1 contractor, all the projects I’ve managed have had Tier 1 contractors as the client. I’ve worked closely with their project teams, systems and processes, but from the specialist contractor side.

I have no relevant tertiary qualifications.

The projects I manage are generally valued at $20–50 million, involving structural steel and architectural packages and larger infrastructure projects.

For those working in Tier 1 infrastructure or involved in hiring:

Would a Project Management degree materially improve my chances of transitioning to a Tier 1 contractor?

Would a Construction Management or engineering-related degree be more valuable?

Would I be better off pursuing another qualification?

I’m willing to study if it will genuinely improve my prospects, but I don’t want to commit several years to a degree if my experience and more targeted qualifications would provide a better pathway.

I’d appreciate feedback from anyone working in Tier 1 infrastructure or involved in recruiting Project Managers.