If I may make some extrapolations….
Dytherous could be related to *Dethero-, an Indo-European root meaning “to hedge one’s bets” which survives in the modern English word “dithering” and perhaps also reflected in the ancient Gaulish “Drutheron,” a name for a 1st century BCE Arvenian chieftain who was well-known for his delaying tactics during the Gallic Wars with Caesar. The -us suffix of course, gives the verb a reflexive meaning, perhaps “to dither oneself,” or it may, again like the Gaulish example, signify a name. Unfortunately, I cannot recall a “Dytherous” in the annals of Greek or Coptic history, but interestingly enough, there is a Detherous, who lived in Heliopolis in the 2nd century BCE, as evidenced by a series of surviving papyrus account rolls now kept in the British Library. He was apparently a dentist.
The next element in the inscription, a lone delta, seems to be the first letter of a now-missing word. That means this could be anything. My assumption is “dramatourgos,” meaning “dramatist.” However, if Dytherous/Detherous is not a name, then the subsequent D may simply be emphatic, drawing us to some inside joke (now lost to us) of the spelling or pronunciation of the first word. Could this simply be a foul joke on some poor Ythero (itself a common name of the Boethian highlands in the 2nd century BCE), who with the cruel addition of a mere delta and enclitic -us to his name, goes from “Proud Shepherd” (cf. Yedderri in Late Tocharian, around the same time) to a name meaning “one who dithers himself.” Tragic in all ways imaginable. And sadly, we will never know.
'Kai' simply enough means 'and' in Greek, both ancient and modern.
The next word, “mini” is a little more difficult, but please bear with me. Of course, the natural inclination (at least for modern speakers of Indo-European languages) would be to read something along the lines of “small” for this, but this is of course confusing our Latin and Greek! In Latin, the min- stem (reflected in words like “minus,” “minimum” and “minute”) means “small” or “diminutive,” but the equivalent in Greek is mikr- (as in “microscope”, “microphone” and “micron”. So we can dismiss this as a false assumption out of hand. This may, however be a form of the word “minon" meaning "months" or a corrupted plural form of "mina,” meaning a “talent of silver.” But it just as easily could be a genitive form of the name Minos, who of course was most famous for constructing the mythical labyrinth on the island of Crete. However, this last possibility is no more than a flight of the most ridiculous fancy, since the genitive form would never immediately follow the conjunction ‘kai’.
Finally, the “outh” seems to be fairly straightforward. The similarities with the proto-Celtic Uth- (also reflected in the Germanic languages and perhaps even the Iberian tongues) are unmistakeable. The obvious connection seems to be with the Welsh “Ythr" which means "terrible." This eventually makes its way into the name Yther, or “Uther,” the legendary father of King Arthur.
However, the emphatic theta on the last line poses problems of its own. Is this a clever parallel to the “Dytherous D” of the first line? It probably should be mentioned that the Aeolians maintained an archaic poetic tradition of taking the first and last letters of significant words and names, in alternating sequence, and using them in the subsequent word in a line of verse. For example, the famous Aeolian poet Aschyllychus (Askilikos to the Mysians) once mused: Moletikos murodin / Spoletiki isnire / Torenemos tundonin / Ieretiko ondire (The walls of Moletikos / [upon which] I once gazed / remain foremost in my mind / until the end of my days). As you can see, each line consisting of two words alternates between repeating the initial letter and the final letter of the first word in the second.
So, my feeling is that this is a fragmentary poem, in a modified Aeolian tradition (in that only the first and third lines reflect the Aschyllychan alternating alliteration). This may give us the following possible original form: