Man this rabbit hole is deep!

I read Acts chapters 9 and 24, and I couldn't find anything that suggests the persons of whom you are speaking preferred to be called "members of 'the way.'" In fact, I don't see that the phrase "the way" is used as a name at all but simply to describe this group of people by others who really don't understand them that well. In chapter 9, the only thing I could find was:

And Saul,...went to the high priest, and desired of him letters...that if he found any of this way,...he might bring them bound unto Jerusalem.

I think the writer is just using "the way" informally to refer to the people he (Saul) wanted to lock up. I don't see that the writer or any of those who were being referred to with the term preferred it. More likely, it is just a generic term used to refer to that group of people, their teaching, and their practice. I don't see that it's an adopted name.

Likewise, Paul himself in chapter 24 says:

But this I confess unto thee, that after the way which they call heresy, so worship I the God of our fathers...

Again, "the way" seems to be simply a generic term referring to the group of people, their teaching, and/or practice. If it were really a name they liked, Paul would probably have used it in his later letters don't you think?

Similar comments apply to the term "Christian," except this is clearly a specific (derogatory) name which, incidentally, means "little Christ" or "little anointed one" rather than Christ-like as you suggest. But it is a name that seems to only be used by those against the group in question. Notice carefully how Paul responds to its use in chapter 26:

Agrippa said, almost thou persuadest me to be a Christian.

And Paul said, I would to God, that not only thou, but also all that hear me this day, were both almost, and altogether such as I am...

Notice that Paul didn't say, "it would be good if you were a Christian," which would have been the natural thing to say, if he liked the term. But he specifically goes out of his way to awkwardly say, "it would be good if you were...like me." The obvious way I see to read this is that he didn't like the term, and knew it was what was used by ignorant people antagonistic to his position, but he also saw that making an issue of that name was not central to his objectives either, so he finds a somewhat diplomatic way to make his point.

and I agree.

Most of what is passed off as 'christendom' has so much mixture from Babylonian/pagan customs and most christians don't even realize it.

Christmas, Easter, SUNday worship were from Constatine and have nothing to do with scripture.