As flaky as the city ordinances might seem, whenever they make the "public safety" argument, that gives them LOTS of power to remove the offending vehicle themselves (usually after a few written notifications). Like a place where rodents might live. NOT to forget about "no flat tires", which means that should first responders to fires might need to move it, they can easily get it out of the way of their actions. And then, the registration also implies it should be "operable" rather than not.
There can also be sections of the ordinance that require the vehicle be parked "on an improved surface". In other words, "not dirt" where the wheels might sink into the ground, over time. As simple, usually, as putting some concrete squares (from Home Depot, Lowes, or similar) under the tires. This can vary, though.
It might also be good to go down to city hall and request a copy of their ordinances about vehicles parked at private residences. PAY CASH, don't give them your last name (so their receipt reflects something like "Jerry, does not wish to give last name), and then do what you can to comply with their items. This way, YOU know the rules the game is played by, so to speak. That is how one of our Mopar club guys did it years ago, in a residential setting. For good measure, get an opaque car cover for it, for "concealment", which can be another issue, too.
Enjoy the car and getting "back to its glory",
CBODY67
NOT to defend them, but there are reasons for them.