Therein lies the problem. There are no "typical stop-sign rules" for two-way stops.
And the statutes cited refer to all roadways - not "Major" roadways.
Around here, "typical stop sign rules" fall back to "first come, first served"

I don't really know the letter of the local traffic statutes, but that's the way practically everyone drives locally.
As far as major roadways or not: I read the CA and OH statutes differently -- I'm not concerned that they don't use the term "major". Since the OH law
does use the terms "alleys, driveways, etc." they are trying to make some kind of distinction. I make that distinction at main drags vs back streets/residential streets (roughly). Others' MMW.
...
There is actually a similar intersection to the one in the OP two blocks from my house. The main drag (only 30 mph, though) is actually two lanes in each direction with a median. Neighborhoods on both sides feed into the main drag. I often find my self in the OP's situation ... me in Car B just pulling up to a stop sign and ready to turn right looking over at Car A who has already been waiting at the median crossover to turn left (at this point, Car A is committed and cannot backup, turn right, and U-turn).
A common maneuver is simply for both cars to turn almost simultaneously -- Car A into the left lane, Car B into the right (which, I know, wasn't available to the cars in the OP). In denser traffic, often one car hand-signals to the other to go ahead and turn. I will always hand-signal to a car that's aiming to turn left if they were there before me

In turn, most often when I am at the stop sign first, I get waved through. Again, don't know the letter of the law here -- we just handle it our own way. Yes, the occasional impatient and/or oblivious person can make things a little hairy if they misread cues or go off in a hurry or something. Such is life.