Two notes here on your debates παιδαρέλια/momči.

1) "Rum millet" as a religious collectivity referred to all Orthodox Christians:


2) On the other hand, "Rum" as an ethno-linguistic category ment only "Orthodox Greek speaker", a Romjòs (Ρωμιός). For example, the traditionally Greek speaking region Rumluk in central Greek Macedonia was named such because it was inhabited exclusively by Orthodox Greek speaking Ρωμιοί:


And for the Momči I apologize but there's only one translation "na Crnomorski":


Rumluk meant "land of the Rum/collectivity of the Rum" just as Shopluk meant "land of the Shopi/collectivity of the Shopi".


Or the traditional Turkish name of the Greek Cypriots "Kıbrıslı Rumlar":


In this sense turkish "Rum" had the exact value of south Slavic "Grk/Gъrk/Grъk" as in the song about "tri ubavi devojke" from Macedonia "edna Grčina, edna Vla(h)in(k)a, edna Bu(l)garka".

3) Before the creation of the Greek state the Turks had no concept of "Greece" nor did they use the term "Yunan" for Greek. When a Hellenic state was established that promoted a new Hellenic rather than the traditional Romaic identity, then the Turks borrowed the term "Yunan" from the Quran, where it was used in order to describe the ancient Hellenes.


So when the Grkoman Vlach Daniel of Moschopolis asks the "alloglot" (non Greek speaking) Albanians, Vlachs and Bulgarians to become "Grkomans" he asks them to become Romaioi and to learn the Romaic language, the mother of all wisdom and to abandon their own "barbarian" languages.