Do you agree that red herring responses and meaningless obfuscation are not allowed in a valid Socratic dialogue? Do you agree that changing horses is not allowed in a valid Socratic dialogue?
The first two, yes. The third - changing horses - if I understand your use of the term correctly, is allowed, as far as I know.

The second presumption is Turbonium's...
But you agree with Turbonium, therefore it is also your presumption. Or do you now say you disagree with Turbonium? If the former, please supply an argument for the alleged unamity of witnesses, or refer to where Turbonium made it. If the latter, you have changed horses.
No. I agreed on a particular point with Turbonium. Nothing to do with unanimity of eyewitnesses.
For the rest I neither agreed nor disagreed with him.

If you admit that your understand or execution of the Socratic method is imperfect, then you might stipulate to the preceding examples under that admission. In that case you should have no problem also stipulating to my assertion that not everything you say or do here is proper to the method you claim to be using. And if that's the case, then our rejection of your arguments may not have anything to do with misunderstanding your method or failing to accept it as valid.
Strictly speaking that is of course true. But of course it is the reasons that I am given for rejection of my arguments which led me to make that claim.
I think the disagreement about whether "changing horses" is allowed is important in this respect.

The point being that it is exactly the point of the discussion to establish what in this context would be justifiable. So I can't define that here and now.
...if the definitions we contemplate are qualitatively equivalent, then it doesn't matter which we choose. But you imply that it does matter, hence your reluctance to commit to any one of them without examination. Therefore we have to conclude you believe that some approaches to measuring the strength of the evidence are better than others. If some are better than others and it's important to get a good one, then by what criteria do you propose to evaluate them?
This is the important question, IMO. I don't have a ready-made answer. I'll let you know when I've got anything to say on it.

Do you admit that among those who express an interest in the amount and quality of evidence for an airliner crash at the Pentagon, there can be found those who are irrational as well as those who are rational? If you stipulate as much, then do you agree it is not worth trying to satisfy the irrational ones? How then do you propose to distinguish between rational and irrational people for the purpose of "justified conviction" according to this evidence?

If the argument above holds, then merely questioning the evidence does not ipso facto qualify one as rational, nor the grounds upon which it is questioned.
No, of course it doesn't. And I agree that it is not worth trying to satisfy the irrational. The point of the Socratic question I proposed is just that: to try to establish how far one's duty to supply evidence in an investigative discussion reaches. If the Socratic question is correctly explored and leads to a usable answer, this will by itself lead to a distinction between the rational and the irrational on this matter. If evidence (of a 757 having crashed into the Pentagon) is supplied that satisfies the criteria that come out of the Socratic investigation, then those that do not accept that evidence may be called irrational.