That is very interesting. However, it seems strange that if X always was an h-sound that Abraham would be spelled Abraam rather than Abraxam. Also there is Melxisedek rather than Melkisedek. I have a grammar book called Learning the Basics of New Testament Greek by Dr. George Hadjiantoniou (revised by Dr. James H. McGee). He presents both the Erasmian and the modern Greek pronunciation schemes in the first chapter (although I never payed much attention to it before). On the pronunciation of X in modern Greek he says "kh, pronounced in a softer way when followed by 'eh' or 'ee' sounds; in a harder way, deeper from the throat, when followed by other vowel sounds or consonants--in both cases harder than the English 'h.'" Of course that explanation is really hard to follow.

Judging Greek pronunciation by means of Hebrew transliterations would not be the best way. Think of composite words as ἔκχυσις, ἐκχύλισις, ἐκχώρησις, etc., which by themselves prove we have to do with two different sounds, that is the k belonging to ek and the x belonging to xusis, xulisis, xorisis... and they are indeed pronounced as two different sounds (not ekkusis but ekhusis, not ekkulisis but ekhulisis, etc). Hadjiantoniou's nuances of the x pronunciation are rather exaggerated. Of course a sound can be 'influenced' by what follows or precedes, e.g. in m and p sounding together as mb. But between χαῖρε and χρῶμα a difference is very small. Having a long open vowel after it, it is natural for x to sound softer, contrary to having a consonant as r - but it is still a h, not kh.

But there are not only the transliterations from Hebrew to Greek, but Greek to Latin: Xristos to Christus. And since they existed together, it would seem that the Latin transliteration would properly reflect the Greek pronunciation. To this end also, Latin transliteration proves modern Greek pronunciation as correct regarding eu since Erasmian pronunciation says eu = oo, but the Latin transliteration of euaggelion is evangelium, proving that eu = ev. Anyway, I'm lead to the conclusion that modern Greek pronunciation is the best, except I think it would be best for me to stick with x = ch in most cases and kinda make a call case by case.

I wouldn't use the word 'prove' in such an environment. Transliterations reflect both languages. Think about -us (Archilochus, Alcaeus, etc) for the rendering of the Greek -os (Arhilohos, Alcaeos, etc.). In any case, the main point, which is evident by this thread too, is that there was not just one "ancient Greek" pronunciation, how the various ancient pronunciations were sounding we can not know exactly, modern Greek style starts already from the time of Plato, is almost completed in the hellenistic era, and is alive, known and certain, which makes it the only possibility for a student to learn a spoken and not an imagined-by-'experts' language.

There is a clear difference in case endings due to the languages, so I wouldn't argue that-os and -us or -on and -um were pronounced the same. But, yes, I see your point overall.