I think you’re fighting a losing battle here, mos-co will sound as wrong to an American as mos-cow sounds to us. I presume both US and UK both used “mos-co” originally, and the US broke away with the newer bovine pronunciation at some point. I’m curious why and when this happened though - maybe the advent of TV or Radio there were some prominent announcers who used that pronunciation and it stuck?

What puzzles me are the elongated “aw” some use in place names like Milan, Prague and Hamburg (“Milon”, “Prog”, “Homburg”) - because they’re not correct in either English or the local languages. I wonder if that came from the realisation that "France" uses that "aw" vowel sound in French, so the assumption is other European languages would be the same (i.e. it's a misguided attempt to be more correct)?

Is that really true? In Russian it's Moskwa afaik so neither of those would sound correct anyway. In German it's Moskau, which sounds like Mos-cow.

The Anglicization is mos-cow.

Using Cyrillic it's pronounced in neither of those two ways that you've written.