The reason I'm asking this question is that I cannot find the readings of each number + counter in a dictionary and the Wikipedia page above is not a complete index of them (like, how is 何振り pronounced for swords? なんふり？なんぶり？). What's more, although dakuten is pretty regular, it's also pretty common for there to be differences between counters. (For example 四本【よんほん】 and 四泊【よんぱく】have different dakuten despite being the same number)
It seems that you are touching the deepest theory of linguistics in Japanese.
What you are asking is 「連濁」(Rendaku) phenomenon in Japanese.
Please refer the following Wikipedia documents.
As I've said, since you are touching the deepest theory of linguistics in Japanese, I'm almost sure that unless a someone is PhD in Japanese who has been working with that Rendaku phenomenon for his career, nobody can easily answer to your question.
If you refer the English Wikipedia document that I've attached, you will read the following.
"Despite a number of rules which have been formulated to help explain the distribution of the effect of rendaku, there still remain many examples of words in which rendaku manifests in ways currently unpredictable."
I did try to answer your question of [Question: Why 四本(yonn-honn) vs 四泊(yonn-paku)?] by searching for some sources,( [source1] [source2]) but it seems that your example goes for the exception of rules of Rendaku phenomenon.
It is definitely 四本(yonn-honn) to read it, but you know what. I've read a story from some Japanese who read it as yonn-pon, and you will see that nobody explains it why it is yonn-honn but they just know that it is yonn-honn.
So yeah, Japanese is like that. How would you answer if someone asks you about English when he asks why the word 'guarantee' is being read as [ɡærənˈtiː] not [gwaranti:]? I hope you could just be familiar with the language itself rather than thinking about its theoretical part. Many problems in language doesn't work like math. The only way to learn language is to feel it, as you feel some music.