I will give a little bit of thought to this series idea, but what I'm generally thinking about doesn't really need to be formal or structured really in any way, beyond the prior agreement by all players that it is to be a quality gunboat game, with a focus on awareness of communication signals - as opposed to playing as though against the computer. That's the fundamental difference in styles.
Devonian, I understand your point, and I would like to expand upon it, using as you suggest the dictionary.com definition:
"the conduct by government officials of negotiations and other relations between nations."
It seems to me that perhaps you focused more on "negotiations" than on "other relations" - I won't bother copying the definition of "relations" here, but I will argue that other relations exist in a gunboat game. So technically speaking, diplomacy is involved. Now, as for negotiations, this is much more difficult to achieve, but it happens. Often this unfolds over several turns, and can be delayed or disrupted by the "I'll take it/You have it" dance over support into a territory.
Look, there is an inherent subtlety to communicating offers and requests and other intentions, and of course it doesn't look like negotiations - especially if players don't look at the orders entered for each turn. To succeed consistently at gunboat, there must be a constant awareness of what is going on around the board, and much analysis of what other players' moves indicate. Which of the other players are aware of the same things you are, and which are playing blind? You see a solo threat and you think you can stop it, but it will require you to move in a way that's sure to be seen as hostile by the nation in between. If he retaliates, he will erase your ability to stop the solo - which will then be guaranteed. How can you signal your intentions, when you don't have a unit to spare for a friendly green support hold? When you can't ask questions directly, but there is a clear awareness of communication by several players, it can be fascinating to see how coordination develops.
I'm not nearly enough of an authority to be writing so much - my words-to-experience ratio is getting dangerously high. I play full press and gunboat and love them both, though my preference is absolutely full press. I am not intending to be the gunboat standard bearer, I just see this argument a lot and hoped to help generate some further discussion. What it comes down to is that there are a wonderful variety of approaches to this most excellent game, and to each his own :)