Thanks for all of your replies. I'm posting again to close the loop and share solutions for anyone who finds this post in the future.
@jeff_strater
This body looks, from the image, as if it was created from a mesh that was converted to BRep. That will always be problematic, to be honest. This shape looks fairly simple, I would re-create it using a Loft, and using the original mesh as a reference when creating the profiles on each end. If you share the design, or the original mesh, we can help show you how.
Yes - you're absolutely correct. Now that I have more experience with Fusion 360 I can see why this is the case. I solved this by importing the shape as multiple IGES surfaces, and using a combination of surface and solid body tools to create a hollow structure.
@jeff_strater
This is the result of a half-hearted 15 minute Sunday morning attempt to re-create the shape using native solid features.
That is almost exactly what the final solution looks like.
I solved this two ways:
1/ Creating rips perpendicular to the body, sketching the hollow shape, and then lofting between them. This was time consuming and tedious, but it worked
2/ I created a solid body, and then used the surfaces as cutting tools to slice that body and remove unwanted material - this was much easier / faster
Thanks everyone for your help!