I have a 78 Monaco. Same car some would say.
Mine was a County Detective car from the county my folks grew up in, in WI. Fortunatly, when it went to auction a guy about an hour away bought it to pull his summer vacation camper and parked it the rest of the time, or salt would have destroyed it. I picked it up 2+ years ago now. I have only seen two others in a 300mile radius, one was closer but had the springs in back holding the trunk lid up(yeah it was bad) and the other was dark green but across lake michigan and the guy wanted way to much cash for it.
All you needed to buy one of these back in the day was be part of a public agency. Police, county, state gov't, fed.... so forest service maybe, but could have been bought as a run around for a town official or something. The town I grew up in bought a mid 90's Caprice police but left it in plain blue and it was used as the City hall/ City Garage business car for taking trips to county meetings etc.
Given you have the "plush" interior with a split bench I suspect this was some official's ride for a couple years.
Not all were 440 cars, some had 360, some were 400. A few states had restricted the engine size even for the gov't agency.
it is not that unusual that it is green. Mine is Starlight Blue Metallic and had a wedgewood blue top with the wedgewood blue interior(called "light blue) The one I saw with the springs through the trunk was cadet blue with a plush interior like yours, and the one in michigan was Augusta Green(I think this is the color of the one from Hunter)
here, this may be handy:
1978 Chrysler Paint Charts and Color Codes
Interior options seem to be a bit all over too, my car has a more standard interior with a front bench, but it has the three spoke rally wheel with the round cap in the middle. I see a lot more with the upgraded interior option(gov't spending lol) like yours.
Parts are a PITA to find. I need a windshield, will likely end up buying new for like $400 because a parts car around here is going to be impossible I think.
People treat the police wheels and caps like gold too. I had the spare in the trunk yet, but previous owner put these crazy chrome salad bowl looking wheels on(never seen anything quite like them) so I went with some old Crager "D" window black steel wheels and chrome lugs. You can fit 275 rubber in back with room to spare(15" rims) and could maybe go the 295 route but then the sidewall has to get a little skimpy.
Find the 1978 Service manual(s) on ebay or something for cheap. I got both for like 15 bucks shipped from a used book store on the west coast. When you go looking, be advised the electrical manual is it's own book. It is it's own chapter "chapter 8". I found out when I got the regular manual and it went from chapter 7 to chapter 9 and when I went to look at the table of contents it has "see electrical manual" in italics for chapter 8. Then I get the electrical manual, and the table of contents says, and I kid you not, "Chapter 8".
Good luck! Keep us posted!