Ok, I haven’t read all the way through. But I have a few thoughts. First and foremost, I think that you would have no trouble at all being understood if you use the terms Conscious dream and non-conscious dream, because they are already used. Second, you are not suggesting giving up old terms, and you would completely understand what people mean when they say normal dream, so, what are you trying to achieve, actually? If it is to start the use of CD and NCD, it’s already been done a long time ago. Even before LD maybe. If it is not to stop the use of the old terms, what should be done with them? And if it is not to convince others to use your terms, then what is it? Seems a little funny to me.
I see your point, that saying ND compared to LD makes LDs seem more difficult. Psychologically, it might be better to say unlucid dreams or non-lucid dreams in order to not make such a fuss about lucidity as to inhibit them. I don’t see the criticism against its accuracy though. ND are more common, and as such are the norm for most people. LDs are special. There are more features to dreams that can be expressed, such as vividness and lenght and such, but what is our interest really? If you strive for long dreams, you will call some long, and some short, and there will also be a range of regular length dreams. If you are only looking for long dreams, you’d call those NDs. The same goes with all aspects of dreams. If you are looking for zombie-dreams, you will have ZDs and NDs. If the dream has no specific interesting feature on display, why not call them NDs? You can’t call a dream a long dream, just because it’s not a lucid dream because it might be short(, or a normal lenght dream). So in the context of lucid dreaming, NDs is a proper term. You could choose to make it more neutral by saying, perhaps, Other Dreams, but it only works in plural. What you call it just depends on how much you want to say. You could call a dream a Long Vivid Random Strange Lucid False Awakening (Dream).
As for what to call LDs themselves. Choosing the right word depends partly on the euphony and cacophony of the terms, and also on what you are focusing on about the dream. To call a dream a Conscious Dream, highlights the state of consciousness, implied to be high. But consciousness does not guarantee that you know you are dreaming. Take Pre-Lucid Dreams for example, they are just as conscious as a Lucid Dream, only you have not yet aquired the necessary proof that you are dreaming. It would be understood from the context what you mean ofcourse, but I tend to make a difference between high consciousness and knowing that I’m dreaming. Usually they go hand in hand, but they are not the same IMO. And technically, we have a degree of consciousness in all dreams we remember, because you can’t remember if you did not have consciousness. Every experience is conscious or it wouldn’t be experienced. “Lucid Dreaming”, highlights the clariry of thought you are expected to have, in order to realise you are dreaming. That is, to not be distracted by random thoughts. It should be possible though, to be aware that you are dreaming and still not have clarity of thought. But then, those are often called low level LDs. What you focus on is really a matter of what you think is important about the dream. The way you define the terms shows that. And if a different word fits your definition better, go for it!
My final words, might be the ultimate solution to the problem, even if it does not make it easier exactly, it does do away with the problem. The terms in themeselves, can have connotations that don’t do the dream justice. And since people might have different definitions of the same term, misunderstandings can take place. The important thing is not whether your dreams with neatly into a specific category. To obsess about that, will take the fun out of your dreams. If you make it your goal to fulfill the requirements for calling the dream you just had a conscious dream, or lucid dream or whatever, you are forgetting the reason you wanted to hae the dream in the first place. It is not about categorisation and technicality, it is about having the experience. And if you want to do it justice, just describe it without putting a label on it! Does it make you any happier to be able to say: “Yes, this dream fulfils all the requirements, I can call it a lucid dream. I have accomplished my goal”? What about the dream itself? Did you enjoy it? If you did, do you care whether it can be called lucid or not? So why bother with labels at all? just say: “I was quite conscious in the dream, I realized I was dreaming, and I had loads of fun”!