Indeed those euphonic changes occurred mostly in
Muromachi period.
This is a bit off-topic, but I'm familier with the change "au to [ɔː]" because, unlike
Kyoto dialect, i.e., standard Japanese at the time, [ɔː] changed to the long vowel "ā" in the later period in some dialects, including my hometown's.
e.g.
行かう (the classical volitional form of 行く) -->
standard 行こう (long vowel ō)
dialect 行かあ (long vowel ā)
さうな (the classical attributive form of an adjectival conjugational suffix そう) -->
standard そうな (long vowel ō)
dialect さあな (long vowel ā)
However, these changes are mainly found in inflections of conjugational words like verbs or adjectives, and it didn't occur on the dictionary form of verbs/adjectives. Thus, 買う/かう (to buy) doesn't change to こう "kō" in the present Kansai dialect or かあ "kā" in my hometown dialect, even though the past form is こうた "kōta" and かあた "kāta", respectively.
Similarly, the euphonic change didn't commonly occur in nouns (except the ones derived from verbs and adjectives, of course). Thus, it would be rare that a location name like なかうみ(中海) Nakaumi changed to なこうみ Nakōmi.
Anyway, if you want to use "mau" for the pronunciation [mɔː], you need to distinguish it from the common pronunciation of まう, which is also written as "mau" in romaji, I think.