Learn English – “I have chosen,” “I choose,” or “I am choosing”

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 agree with the comment from @PeterShor that constructions 1-3 all effectively mean the same. Construction 4 is just awkward, but I wouldn't interpret it differently from the others.

On the other hand, they all seem somewhat long-winded, and could simply be written as:

If ever a vote were held on X

As regards your four 'meanings':

1. I think the use of "If ever" rather than simply "If ..." is what conveys the possibly hypothetical nature of the action, and therefore that hypothetical nature carries through all your constructions.

2. To convey your second meaning, I would use the past perfect tense:

   If ever there were to have been ...

3. To convey your third meaning, I would omit "ever" and write:

   If, theoretically, ...

4. To convey your fourth meaning, I'd use something like:

   If ever we were actually to hold ...
   If ever a vote were actually to be held ...

In summary, no, I don't think that the constructions actually convey different meanings, and, if I wanted to convey such nuances, I would use additional words and/or different tenses.