The "reframe the conversation to the thing I want to talk about" - man, that one's frustrating. I don't have a polite way to stop that one yet. I think some of it is just that we all pick up traumas and trigger words, and you've gotta recognize when someone said "banana" that doesn't actually mean "the thing I slipped on five years ago."
Selective doses of being impolite can be extremely effective, especially when you're otherwise very polite.
(One of several variants: <https://quoteinvestigator.com/2015/01/21/offense/>)
The most effective method I've found is making that person responsible for resolving whatever the issue is. Not always possible, but especially when it happens in group settings, some verbal judo can work even if you can't "officially" task them.
(Make sure to memorialize that in an email afterwards, or it will probably retroactively never have happened.)
"So, I see your business model is to make widgets. But ... uh... I don't really understand these ideas but that's called capital intensive, right? So, you're gonna have a factory, with a bunch of workers... in San Francisco? Won't that be really expensive, and ... uh, I guess that means your profit margin will be small? Could you put your factory in Kansas?"
(paraphrased but essentially accurate question I asked when being pitched by a hardware startup at a major VC that I advised)
But more to the point, I find that asking for clarification is the best tactic in the aforementioned circumstances. That way, you avoid having to make accusations. It removes all pretext for getting defensive and focuses the discussion on the substance and merit rather than the character flaws and lack of speaking skills of the other. If the other person starts to get unjustifiably angry, this reflects poorly on them, not you, so there is no need to feel any guilt. Be honest and never lie. Do not pretend to understand someone just because you think asking for clarification will make you look less competent. Maybe you are less competent, in which case pretending to competence you don't actually have is dishonest and unjust. You also close off the doors to learning. And if you are competent, then there's nothing to worry about. Bullshitters feed off pretense, and honest people are dismayed by it.
A few suggestions for getting more value out of your observations:
* in the moment, particularly if it's heated, you won't make a ton of headway unless you really know the parties involved and know how to frame "i think you agree with each other" well enough to be heard over the argumentative mindset. Instead pointing it out to each party individually in a later/follow up discussion can help a lot!
* If you have a good "people person" mentor or manager, just pointing it out to them can often result in positive outcomes, because they can take it on themselves to have the discussions in the background or if you ask for it, mentor you in how to get that across in a well-received way.
* sometimes when people are arguing with each other in agreement, the issue is usually semantics and someone (or everyone) has a different take on some word/phrase/name whatever being used. A good tactic is to try and identify where that bit of disagreement is and play dumb (it works best when you're in a "junior" position but can work in any situation) and say something like - "wait, sorry to interrupt but I don't quite get the difference between foobar and barfoo can you help me understand?" and then when they explain to you, the neutral third party, they'll come to the realization that they are arguing in agreement after all.
I've been in your shoes before and the above advice helped me get going so I'm passing it along. For me the difficulty in relaying the info came from a couple places:
* I was afraid of speaking out of turn, or looking dumb. It turns out that the "dumb look" i was afraid of is often interpreted as "wow this guy is asking smart questions", and at worst it's interpreted as "this guy needed a bit of a different explanation to grok it".
* I didn't realize that people don't need to understand that I was seeing them argue in agreement or avoid the question. I just needed to ask my own clarifying questions until everyone got the info/agreement they needed. If they get that I was driving at "arguing in agreement" or if they think I resolved a conflict, it doesn't matter - the goal of "we're all on the same page" was successfully reached.
I've still got a lot to learn in this whole area, but even trying to address those things often helps smooth out the rough bits and is useful. HTH!
If you ask a question and someone is scornful ("you should know that already!"), First time it's on them, second time it's on you, third time update your resume.
I don't use it so much for the teasing out agreement or highlighting problems angle though - one of my goals is setting the accepted threshold for dumb questions low enough that junior/newer or less confident team members aren't afraid to ask their own "dumb questions". Those questions are usually more important than mine, and teams that don't have that "no question is too dumb" culture are often dysfunctional or heading that way.