>it's widely accepted that Shor works. We simply don't have hardware to run the full version.

I can't quite get this - surely until we have an execution on the proper hardware we can't accept that it works? There are engineering problems to resolve before we can be confident - perhaps they can be easily resolved, but so far they haven't.

I would be very curious to learn what the barriers to a demonstration of Shores on an arbitrary 8bit prime are...

It's mathematically sound and the quantum primitives it uses are well understood.

The limiting factor in practice, as with everything quantum, is noise. You are right -- we don't know for certain until it's implemented. I suppose it's part of a bigger question: whether quantum computing will work at all. My knowledge of quantum hardware is limited, so I can't really comment more on this.