Hey Jason!
So glad those tips helped you identify an industry centroid that may be a contributing factor. Way to go! Some thoughts on this:
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Go into this knowing that it can be VERY difficult to overcome something like this and that your best bet here is likely to be a full, professional audit by a skilled Local SEO consultant. A good place to look for one is the Contributors box on the right side of last year's Moz Local Search Ranking Factors. Here are some questions for you to ask yourself, either for your own purposes, or to share with a consultant.
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Are you 100% certain that you are located inside of the official city limits? As I mentioned on your other thread, do the Maps lookup of your city name and be sure you are inside of the pink city border instead of outside of it. If you're outside, then the goal of ranking in the Local pack for that city/keyword combo is likely out.
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If you are inside the city borders, how far are you from the industry centroid? Are any other players as far away as you are and still ranking in the top 10 or so results?
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If so, do an audit of any competitor that is as far away as you are, but is managing to rank in the top 10 on the Map. Identify every piece of information you can that might be contributing to their rank (age, domain authority, reviews, vibrant content, citations, etc.). Mine this data to see if there is a pattern or a weakness you can identify that you would be able to use to your advantage, with the goal of helping you get into the pack.
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Do not make the mistake of thinking that the industry centroid is the sole cause of what you are experiencing. If you're outside the city borders, then, yes, that's probably the main cause, but if you're inside the borders, a business which is supremely strong enough should have hope of overcoming an industry centroid bias. But, remember, there may be multiple causes contributing to low rankings.
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Finally, don't forget that user-as-centroid is likely to overcome industry-centroid bias, in that your customers who are physically closest to you on their phones may be seeing a different set of results, which do include you.
Just some quick thoughts. Hope they help!