I'm pretty sure that since the state implemented standardized requirements that you don't need to get letters of recommendation anymore. The towns can ask for it but you don't have to supply them.
If the town refuses to move on the application without the letters , then you call up the state police and tell them that the locals are requiring more than the state requires and you'd like to do your permit appilcation with them.
I don't know if that would work (or how quickly) but it sucks for you that your local police are asking for things that other towns don't. It makes it a double standard.