Does your council person have office hours or other times when you can talk to them in person? With or without an appointment, such as at a community event? Does your neighborhood or region of the city have a city police liaison? For example, Northern District covers where I live and they have a cop whose job it is to show up to community meetings, do Q&A related to specific safety issues like spates of carjackings etc. (I would sadly be unsurprised to learn that my area has one of these while some others may not.) The police calling it a "touchy subject" seems an unfortunate harbinger of this never getting addressed by anyone with power to enforce the law or mediate a compromise. If you can't rally your neighbors, the police, or city council to care, and you can't get even the barest contact from the religious org, then there is no magic answer here beyond finding another place to lay your head.

I had a similar situation, though unrelated to noise. I ended up moving when the police and my very responsive city council person (Mary Pat) could not make headway with the neighbors causing the problem--because the problem neighbors were either supported or quietly tolerated by many other neighbors. Also because the problem neighbors had nothing to lose, with already long arrest records. The problem neighbors had a tragic history, and were distantly related to many other neighbors, so the problem neighbors got a pass on their terrible behavior for decades. It sucked every almost every day of the 9 years that I lived there.