Assistance in showing computational equivalence between software and hardware computing systems
These issues are clearly and accessibly covered in Sanjeev Arora and Boaz Barak's Computational Complexity: A Modern Approach, specifically in the chapters "The computational model and why it doesn't matter", "NP and NP completeness", and "Boolean circuits" (respectively chs. 1,2,6).

Very generously, an on-line draft of this book has been provided by the authors ... this has been a big help to me in my own researches!

From the viewpoint of complexity theory, the various theorems and proof technologies in Arora and Barak's exposition provide little grounds for  "divorcing the process of computation from the agent of computation"  (in the phrasing of the question).

From a regulatory perspective, however, it is well to keep in mind the legal maxim:


  "Justice is the tolerable accommodation of the conflicting interests of society, and I don't believe there is any royal road to attain such accommodation concretely."
  
  --  Judge Learned Hand


In real-world medical practice, and in many other regulatory contexts such as aircraft safety, commonly it is legally and practically necessary to distinguish between hardware and software, even though all parties recognize that the mathematical foundations for this distinction are highly imperfect.