As far as I can tell, the mora in ancient Greek applies only to the vowel part of the syllable, that is, the part of the syllable which can carry sound. It looks like χρόνοι apply to the entire syllable and are more related to syllable weight, that is, heavy or light.
The mora as develped by the Prague School seems to be more of a theoretical analytical device that has been found to be useful in ancient Greek most importantly in allowing a concise version of the accent limitation law of ancient Greek: Not more than one mora may follow the contonation. Of course the notion of the contonation had to be introduced as well in order to get this to work.
I believe that for ancient Greek, the inclusion of the closing consonant of the syllable is not allowed, which differs from the treatment in Latin.
I have this from Auer, in which he discusses mora counting in some pitch-accent languages, but explicitely notes that this does not apply to ancient Greek. Auer, “Some ways to count morae”, 1989.
“In some of the languages with musical accent (but not, for example, in Classical Greek), this second mora may be part of a long vowel, or a consonant. Long vowels must be split into two parts (= morae) so that stress can be placed on either one of them (falling or rising), and vowels and consonants must be treated alike so that the proper generalizations can be made.”
The picture that I am getting for ancient Greek is that only one mora in a word could have a raised pitch. There was definitely a glide back to base level after this mora, and possibly some sort of rise from low to high in the preceding mora. But those preceding and following morae did not alter the fundamental property of only one mora having a raised pitch, and it is important not to think of this frequency modulation as something like what happens in a tone language, in which pitch contour over a syllable is used to differentiate otherwise identical syllables.
Thus it is not correct to picture the circumflex accent as being something like the fourth tone (the falling tone) in Mandarin Chinese. It is simply a raised pitch on the first mora. Similarly the acute in a long vowel or diphthong is simply a raised pitch on the second mora.
Making the entire long vowel high pitch in the case of the acute leads to something like the first tone in Mandarin Chinese (the high level tone), and so is not correct.
In fact I have read some stuff conjecturing about how the transition from pitch accent to stress accent might have taken place in Greek, and one idea is that the circumflex and acute in long vowels or diphthongs started to become indistinguishable due to the raised pitch covering the entire vowel.