The rules (although I'll argue none are needed, see below) really are quite simple: yes, what I described above works recursively: there is no difference between a counter-interrupt and a counter-counter-interrupt.
All of this hinges on and ends up being managed by each person giving the other a certain amount of benefit of the doubt, that any of these interrupt-related actions are being done out of a genuine desire to communicate effectively (vs someone trying to make some kind of power play). With that trust in place you don't need to know any "rules", this all emerges quite naturally.
My assertion is that it is very very easy to miss "easy rules that were emergent and are working well" with "I didn't realize there is a social hierarchy here that I'm massively benefiting from." Or, worse, "there could be consequences for my interrupting this person, I should keep quiet and let it go."
But again, this isn't going to be the case among people who know each other well. My family and I are interrupters, and we've been at it for decades now - none of the issues you're raising would apply.
In terms of knowing when/whether you can interrupt the interrupter/counter-interrupt/etc., see my other post in this thread about how the time of interrupters talking over each other is a signal to both that's constantly evolving (because the increasing time is an increasingly strong signal).
For certain. I'm less arguing that it isn't a conversation style, than I am that it is a dangerous one. Even in families, it is easy to see this form lead to resentment between folks. Or a contest to be last person talking. In a large sense, mansplaining is similar. Echoing back and explaining things even to people that know them isn't, itself, bad. But it is very easy to portray in a negative light and should not be the assumed default.
Now, I fully grant that the largest poison in all of this is the transactional view of conversation. The interrupt style is still predicated on an open transaction that will eventually commit.
> My assertion is that it is very very easy to miss "easy rules that were emergent and are working well"
You are right, at least for people who have poor social skills, are emotionally unstable or immature in some way, including people with autism, ADHD, dementia, children, etc.
With such people arround, it may be better to have clearly defined rules for who speaks when. The same goes in situations where people come from very different background or there are very low levels of trust to start with.
The better a group of people are at communicating in a cooperative manner, the fewer hard rules are needed.
All of this hinges on and ends up being managed by each person giving the other a certain amount of benefit of the doubt, that any of these interrupt-related actions are being done out of a genuine desire to communicate effectively (vs someone trying to make some kind of power play). With that trust in place you don't need to know any "rules", this all emerges quite naturally.