I've had similar residency issues, albeit at a city/county level: my previous residence was not in any city, but the same street continued into a nearby city which stupidly repeated the numbers on same-named street (different ZIP code "didn't matter").

Because my ID had an address that was considered "valid" in that city, I could use their trash/recycling facilities without any difficulty (and did because they were closer than County's).

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I currently live in the reverse situation: I now actually live in that aforementioned city, but my new DL address requires me to bring in a city wastewater utility bill, for verification (for "city residency" == free trash/recycling).