Yes, that's past perfect. Perhaps the problem is just that you don't want past perfect tense. The simple past will inform the reader of the same facts:
On January 17th, our team represented [organization name] at [place].
You might favour the past perfect here if you were then going on to describe how that effected another event in the past, later than that one:
On January 17th, our team had represented [organization name] at [place], so we were already well-known there when we went in March.
You don't have to use it in this case, since the date makes the relationship between them clear. Consider without the date. The first two give exactly the same information:
Our team represented [organization name] at [place].
Our team had represented [organization name] at [place].
The second leads me to thinking "and then what", but that's no bad thing if you're going to tell me "and then what" later on. When we do bring up a later event, this jars:
Our team represented [organization name] at [place], so we were already well-known there when we went in March.
(In reading that, I tend to respond with "wait? what? when? are we talking about the same time here or what?").
This flows:
Our team had represented [organization name] at [place], so we were already well-known there when we went in March.
Okay, one event in the past followed by another event in the past. Perfectly understandable.
As a side note, does it matter if it's British or American English?
I've heard it said that American English is more tolerant than British English of using the past perfect with a stated date or time (as you have done). I'm not convinced that this regional difference exists. I'd read it as valid, but unnecessary. (Though my English is neither American nor British, of the two it would be closer to British on most things).
I have a question.
Present tense. Right now I have a question.
I have had a question
Perfect tense. At one point, I had a question. It may or may not be true that I still have it now (might be made clear from the rest of the sentence).
I had had a question.
Pluperfect. At one point it was true that at an earlier point it was true, that I had a question. "I had had a question for some time, but I never got a chance to ask it".
Now, in each of these the verb have is used once in the sense of "to possess" or "to hold" and in each of the second two it is used as an auxiliary to modify that other have.
You propose.
?I have had had a question.
Which we would presumably have to interpret as some sort of super-perfect stating that at some point it was true that at an earlier point it was true that at an earlier point it was true, that you had a question. It's not clear what you are saying about the current state.
As such, you've just created a non-standard variant of either the perfect or the pluperfect, but you leave us confused as to which - and imply that you are confused about the matter yourself.
You suggest it might be better as:
?Having had had a question, I asked it.
But this presumably would mean that it being true that at one point it was true that at one point you had a question. Again, it's not clear just what this is supposed to mean, and one possible interpretation has this as impossible (because one way of untying the knots leaves us with the suggestion that you no longer had a question at the time you said it).
In all, this reminds me of some comic nonsense writing that has been done - sometimes well - but were the whole point of it is that it was not good English. Barring that goal, none of this makes any sense.
You talk about "unique time travel situations", and I could see someone deliberately engaging in this sort of abuse of auxiliaries to describe that. Still, the implication is "this time travel has so messed with the logic of causality that English grammar can no longer work to express the resultant mess". Once you're doing that then you've deliberately thrown the rules of grammar away for effect anyway, so asking if it's grammatical is not just besides the point, but counter to it.
Really though, this is not grammatical English. Nor is it a useful construct to anyone who perceives time and causality as being related things.
Best Answer
If I were reading a story that began
I would expect the following things of the story:
(1) comes from the use of past knew in the first sentence; one cannot use the present perfect construction with a dead subject or object, so using the simple past is a tipoff that they're dead.
And the time lapse is only 15 minutes, well within the narrative scope of the story, whence (2).
There's a (3), as well, but it's just a flag to watch for while reading -- Mr. Brown's death may be a red herring, and merely a way into a different story, rather than being the point of this story.
I don't know whether that helps, or not.