I would also be putting my efforts into Ads and organic. Proximity is so important that in competitive areas it's truly exceptional to see a listing too far out of the PJ rank cor competitive terms.
That's why it's so tempting to go against quality standards and create listings that use addresses that are not the actual business address, or use names that are not the actual business name. But, this is a risky strategy. Especially in competitive areas, it's very likely the listing will be reported by someone with knowledge of quality standards. In the case of incorrect address information, folks also use listings for directions -without calling first because they already have an appt. Needless to say, these clients would be pretty angry when they can't find the location, which then can in turn hurt the credibility of the business.
It's best to focus on strengthening your overall presence for the city, as well as the neighborhood, and counsel your client to have the best reputation possible across the board. If they become known as the best in City-area, that MIGHT be enough to break through to the higher results for searchers who are farther away from the location.