Your examples are correct.
Well, Robert, you know, the easiest thing for a native speaker would be just to comment a specific example, whether it sounds naturally or not. Or if there is any difference in meaning.
But you are asking a general question, and it is quite difficult to formalize some rules for it.
First I felt ready to say it is an incorrect usage. But later I changed my mind. So, let's try to examine this specific example.
As Robert noticed, "Я никогда не забуду" is the only correct option if taken out of context. At least, it is how it seems to be.
We usually say: "Я никогда не забуду тебя / свою первую любовь / твою доброту / это путешествие etc." In all those examples, there is a single thing which one promises to never forget. So, it can be (in possibility) only a single event of "forgetting" that thing. Let's imagine this possibility in the future timeline:
I remember Valda's help. -- I still remember Valda's help. -- I forget Valda's help. -- I do not remember Valda's help anymore
As you can see, the very moment of "forgetting" has zero time-duration, and it is a single event which separates the two states: "state of rememebering" and "state of non-remembering". And what the speaker actually does is that he promises this single event will never happen: Я никогда не забуду помощь ВалдыI think, it explains why the perfective is the only option for those examples.
However, Valda proposed another interesting example: "Я не буду забывать их". At least to me, it may seem unnatural at the first glance. However, later I found examples where it suits fine:
Imagine a child promises his mother: "Я не буду забывать чистить зубы по утрам" (I will never forget to clean my teeth in the morning).
What changed? The fact is this sort of "forgetting" is different from the first one. It is not something which you remember and then suddenly forget forever. It is something which can be forgotten to be done for a specific occurrence, but later one might not forget to do it etc.: on Monday I forget to clean my teeth, on Tuesday I remember, on Wednesday I remember, on Thursday I forget again
So, we face to the "imperfective iterative" in this case. By saying "Я не буду забывать чистить зубы по утрам" the child implies there will be no any single iteration when he forgets to do it, he will remember it every time he has to.
Therefore, Valda's phrase is correct if she means she will remember those subtleties everytime she speaks Russian: there will be no any single event I forget to use the proper verb aspect - that's what her sentence means.