Top of your to-do list should be getting good accurate information about state law on these matters. You should read the law yourself because in at least one Nebraska city, the Council got wrong info from the city attorney and the city has a massive legal exposure as a result.
Nebraska state law says if a community wants such a restriction, maximum distance is 500 feet and it can't be retroactive. We find that most such proposals are pushed by someone who wants to force a registered citizen out of a home. State law says you cannot do that.
Across the state and nation, residency restrictions have proven to be utter failures (your police chief seems to get that but of course he can't say that publicly because he is afraid of people who are afraid of registered citizens).
Alexandria, Nebraska, last year decided AGAINST residency restrictions because they are of no use for public safety and the ACLU advised Alexandria that it likely faced a costly legal challenge. Here are some useful links on this topic: