Eutectic,
I think the problem is not unlike that which confronts those who wish to impose robotics on shop fab pipe assembly. You have to tightly control every single variable so that you can minimize the number of programs. In this case you would have to tightly control every single variable to minimize the scatter band.
Meaning, material chemistry, base and fillers (especially with alloys), fit up, preheat, base metal thickness, filler diameter, automatic welding with locked parameters, and much much more. And this just for a single pass weld. And you might have the ability to roughly graph a result. Multipass welding complicates it even more. Travel speed has to be exact, bevel angles, bead shifts, etc. And I haven't even reitrerated the testing lab variables. Notch radii, fracture rate, exact temperature control, etc.
And keep in mind with carbon steels martensite is not an issue. You are talking volume percents of acicular/polygonal ferrite, etc. Ultimately you may be able to get there but then what do you have? Mountains of lab data. Or lab data for a very narrow range of variables. And lots and lots of money spent. Much like robotics.
Not something that is practical on a shop floor.
What you would learn, which could be a great deal, would be academic.
I think the fundamental error in your thinking is trying to squeeze precision out of two inherently imprecise methods. HJ and CVN's.
Even Section IX, which is considering the application of HJ, is only trying to get in the neighborhood.
And no, heat treat can significantly effect CVN's. But it is notoriously unpredictable with any precision. The thought process is one of saying that if I do these things I have reasonable assurance that I can maintain a minimum standard, that my test will reflect my production. It is not one of precisely determining the result. I don't think that can be done.