Earlier quoted context omitted.
Without much knowledge about the process: Is it a problem to have it handled via some centre? I.e. you're asking X to dispatch all of those requests for you which would free you up to drive? (And get either one of those calls connected directly to you as needed)
Exactly this. I spent decades as a FF/EMT and that's the way it was typically done. I did however, often carry a Baofeng programmed with _all_ the services with which I was likely to interact as a backup: MedEvac, EMS, law enforcement and fire services. Yes, I am a licensed ham operator. The problem is there is no national emergency interop frequency plan, each state, county and city does things differently.
Each state/county/etc. may have different licensing, but they are also encouraged to program the NIFOG channel plans when space is available on radios.