Everyone is already subject to the law of the land, and therefore 'civvy' law. However, as I'm sure you're aware, there are peculiarites within the military, that turn what would be a mundane civvy event into a military offence. For instance, my boss is a complete throbber, so I regularly tell him to poke it. I might take a different tack if that were my Pt Cmdr.So bin service plod and make everyone subject to civilian law
CivPol already deal with peculiarities within the civvy system, that sits outside of the conventional. When I was in the job, my last posting was on a firearms team at Heathrow (LHR). LHR itself, and a vast amount of land around the airport, is all private property, and as such, there are significant amounts of byelaws that police can rely upon in addition to the law of the land.
The military could be seen the same way in that, there are significant peculiarities and challenges associated with policing it. That's merely a training need and could easily be addressed.
Similarly, Paramedics, Docs, Nurses, Dentists, Pilots Drivers, Mechanics, in fact, the list is huge. All of these professions, could be encouraged to sign on again under the correct incentives.