Do they have their own Modern version of the Greek NT that uses the monotonic system?
That's a good question. I have this texthttp://www.orthodoxmarketplace.com/bibles/greek-modern/isbn-9607847172-tgv-anc-greek-wedding-edition-parallel-nt-leather.html
which has, on facing pages, the Koine Greek New Testament and a Modern Greek "translation," The Koine GNT uses the regular accents, while the Modern Greek rendering uses the monotonic system. I have several other Koine GNT's that are published in Greece, and none of them use the modern monotonal system with the ancient text. I don't know if such a thing is available. It seems this would be useful for some Modern Greeks who never learned the old system with circumflexes and graves, but maybe it is assumed that anyone who wants to read the Ancient text needs to learn this system. The old system is not really hard to read, but I think on a subconcious level it slows one down a bit, and it is cumbersome to reproduce in typing.
I believe that a montonic Koine GNT would be easier on the eye and easier for NT Greek learners to learn to read. The only real argument against NT Greek readers who want to do away with all the diacritical marks altogether (and I'm not quite in that camp) is that one will still want to know which syllable to stress. The monotonic system would do this. People THINK that the rest of the diacritical marks are helpful because that is what they are used to, but I maintain Greek would be easier without them.
If I recall correctly, didn't short/long vowels disappear by the Koine period as well? If so, then the circumflex would be useless.
Even if they didn't, many people today read Ancient Greek with a Modern or Buthian προφορά which largley blurs the distinction between long and short vowels. The diphthong αι is pronounced like the e in pet, which we would call short, and omega and omicron are more or less conflated. The real value of the circumflex is in showing where contraction took place, but I'm not sure this is worth retaining the current system, at least for Koine texts.
That's my next question. If Buth is right that rough breathings dropped out by the Koine period so that every vowel was pronounced smoothly, then why do our standard Greek NTs still have them?
Well, my problem is more basic than that. I personally retain the difference between rough and smooth breathings in speaking Greek, but all I am saying is, in printed texts, retain the rough and get rid of the smooth. I've made the point that in many places on line and in small printed texts, one cannot even tell if a mark is smooth or rough, whereas if you got rid of the smooth, it would be EASIER to make that distinction.
We've discussed stuff like this before on the old B-Greek, but not (yet) to the point of nausea.