These are all good descriptors.
@skribs , what is your motivation for a one word descriptor? Your list of kicks is all multiples or combinations. Add the plethora of variety off a roundhouse kick (any kick) and confusion can ensue without a detailed description. Are you building a progression from belt to belt?
When teaching the kick in combination do you break down each kick first? This helps in understanding how to marry the two kicks together.
I/we try to use the universal terms like reverse, lead, step, walk, etc...
I also think learning terminology requires consistency in terms. So if you say 'throw a roundhouse kick' does that adequately describe the kick you intend? Probably not.
I want to get as accurate as I can with as few words as I can, so that I can efficiently communicate drills. The way I see it, the less time it takes for the class to understand the drill, the more time you have to actually drill.
At my school, #1-3 in the OP would all be described as "roundhouse kick, roundhouse kick", which sometimes leads to confusion. Yes, there are a lot of different ways to describe kicks, and a lot of variables at play. The more I can reduce those variables, the more efficiently I can explain something. I have to agree with what
@Earl Weiss said regarding general Choi - precise terminology is key.
In addition to martial arts, I also love gaming. Board games usually have "keywords" which will always mean something precise. For example, even though "Attack" and "Damage" might seem similar, in many games "Attack" is the chance to hit, and "Damage" is the amount of damage you deal when you hit.
Take this card from the popular card game, Dominion. What happens when you play this card is you draw a card, you increase your action pool by one action, you increase your buy pool by one item, and you gain 2 coins that can be used as money. But what took me a very long compound sentence to write, the game does in 3 words and a symbol. It does this because "+1 Buy" always means the same thing, no matter what card it is on. These are all keywords (even the icon) which let you quickly determine what the card does, and lets the game maker use a bigger font so it's easier to read.
What I want is the ability to quickly communicate common combinations. And 3 of those 4 are going to be pretty common.
A word of caution: I mentioned 'mashing up' your own term. While that would work within a specific school it would not work anywhere else. Could prove to be a dis-service to the student.
The school I'm at already has a different vocabulary from most schools. While I understand the concern, it's the least of my concerns. If a new student comes to my school, I'll understand that they probably learned things different at their schools. And if one of my students goes to another school, the skills are the most important thing I want them to bring with them. If they have a great roundhouse kick, but they're treated badly because they call it a "roundhouse kick" and not a "turning kick", then I would expect they would find a new school that aren't a bunch of blowhards.