But of course they would know what to do with V1, because there would not be any node label at that location. It was an error in the first place to give that point a V1 node label. On a properly annotated schematic that point would only be identified as a supernode offset voltage from the ground reference.

And this person that knows NOTHING about EE stuff is then going to be expected to know how to identify and use "a supernode offset voltage from the ground reference" -- sure sounds an awful lot like EE stuff to me. Even just giving them a cookbook recipe like (Σ{Vnode - Vadjacent}/{resistance to adjacent node}) is having them do the EE stuff.

The point is to divorce the EE from the Math. Let someone that understands the EE stuff apply the EE stuff to come up with a set of equations that embodies ALL of the EE stuff, with as little of the Math stuff as possible (i.e., just the set-up with little or no manipulation, even the simple and obvious stuff). Then let someone that understands the Math stuff apply the Math stuff to solve the equations, without ever having to deal with ANY of the EE stuff. It doesn't matter if it happens to be the same 'someone' in both cases -- humans are lousy at multi-tasking; they are far better suited to focusing on one thing at a time. So focus on the EE first and then focus on the Math next -- don't mix the two.

It sounds to me like you are actually breaking the process into three steps.
EE Stuff:
1) Color code and annotate the schematic.
2) Extract the equations embodied by the color-coded and annotated schematic.
Math Stuff:
3) Solve the equations.

I have NO problem with this whatsoever. In fact, it is the process I use (except I almost never do the color coding because I've gotten comfortable enough that I don't need to). I didn't mention it explicitly here because the TS did a pretty good job of annotating their schematic, but I'm always harping on the need to annotate the schematic with any and all symbols and variable definitions that are used throughout the work.

 

The point is to divorce the EE from the Math.

We seem to be in total agreement except for the actual point where EE stuff transitions to Math stuff. My opinion is that writing node equations is a simple regularized procedure that anyone can be trained to perform if given a properly annotated circuit diagram. Whereas you think that the derived node equations should be handed off to the Math Dept for solution. Nevertheless, it is a simple task to write the node equations if the circuit diagram has been properly annotated, and it seems invariably true that if someone is having difficulty with obtaining/solving the node equations, then that is due to a lack of proper EE work in annotating the circuit diagram in the first place.