The problem with your questions about pH is that the main species involved
is NOT (known to be) a sphere. Thus, we do not have a well defined way
to include "protons" into the EnVarA scheme. (and of course we do not know
yet how to include the chemical reaction which buffers pH, or the nonionized
species, or the hydroxyl ion).

Thus, I would not know how to proceed with what you want to do.

I do know the only approach that (in my opinion, others will disagree for sure)
will work.

1) DEFINE pH by an experiment NOT a theoretical discussion

2) IDEALIZE the experiment

3) WRITE a variational description of the experiment

4) SOLVE the EnVarA description to provide an OPERATIONAL definition
of pH, proton activity, hydroxyl activity, unionized buffer activity etc. OPERATIONAL
means that the dependent variables just listed are written as functions (ONLY)
of measurable quantities (no theoretical constructs).

5) USE the EnVarA analysis to address practical issues like you raise.


About your (understandable) desire to use an incremental approach.
I wish (a) I could do it  (b) it would work.

(a) I am unable to do that because I do not have the "finger feel" for pH
that I (more or less) have for ion channels.

(b) the attached papers show that for a closely related subject (the 'law of
mass action') NO FIX UP IS POSSIBLE. Rather, the entire definition of
the law of mass action must be replaced by an analysis which deals
consistently with ALL the energies and forces involved, namely with
the GLOBAL electric field, nonideality of various types, and electrodiffusion
which is ALWAYS involved away from equilibrium when chemical reactions
actually occur. 

In my view, no fix up of pH will be successful.

If you view this as unnecessarily pessimistic, I urge you to look at

Hünenberger, P. and M. Reif (2011). Single-Ion Solvation. Experimental and Theoretical Approaches to Elusive Thermodynamic Quantities. London, Royal Society of Chemistry.

This fantastic book shows that after something more than a century we do not know
how to define the property of sodium in a sodium chloride solution. This is completely
understandable in the view of a variational approach. There we see that "everything 
interacts with everything else" and the idea that NONconsistent NONvariational
models could define a single ion property is laughable. One obviously cannot describe
water flow from a shower, or airflow over a wing of an airplane, or sound distribution
in a concert hall by such nonconsistent models. Every model would give a different
answer which is exactly what happens with ions in ionic solutions.


and what happens with pH (in my opinion)

I do not believe a fix up will work.