i dont know how Rabbi miller, tzl would answer your question wolf.
he might say no, under such circumstances a person should not daven loudly.
i could also hear him saying to the person who is bothered, it is proper to daven loudly and if someone is bothered he needs to work on himself.
i would guess that if someone asked a loud davener to please keep it down because it was bothering his davening Rabbi Miller, tz’l would agree that he should daven more quietly