I believe one reason why it is difficult to ascertain the etymology of μοναρχία stems from trying to understand this concept in 2-3 languages (Greek, Latin, and English) and we also have to contend with the dual meaning of ἀρχὴ.
Lewis-Short Latin Dictionary defines monarchia as "I.absolute rule, monarchy (post-class. for unius dominatio, imperium singulare, regnum, regalis potestas), Capitol. Max. and Balb. 14; Tert. adv. Prax. 14; Lact. 1, 5, 23."
The Latin form is equivalent to the Greek μοναρχία. Furthermore, we know that the Greek word has the same basic definition according to LSJ Greek-English Lexicon: monarchy or government by one ruler. The word can also reference the "supreme command" of a military official.
It appears that some fathers in the early church began using μοναρχία in the sense that Jurgen Moltmann discusses: the word came to mean divine unity. It referenced God as the supreme origin and principle of ta panta.