Hi BigChad2!
Great topic. One thing that might be helpful to you would be this year's Local Search Ranking Factors survey of some of the best Local SEOs in the world:
https://moz.com/local-search-ranking-factors
You'll see that quality of inbound links to domain and domain authority of website are both top 10 local pack ranking factors and, if you drill down, you'll also see things like HTML NAP matching GMB NAP, diversity and quantity of inbound links to domain, page authority of GMB landing page URL, topical keyword relevance of domain content, etc. all being cited as top 50 factors. So, these are all organic factors that industry folks believe impact local pack rankings.
That being said, I'm not aware of any recent formal case studies, per se, that have taken screenshots of the correlation between high organic and high local pack rankings, but this would be something you could likely easily pull together if you needed to do so to illustrate/prove a point.
To undertake such a project, I'd do a variety of searches in cities across the country, such as "Dentist Santa Fe", "Dentist Boston", "Dentist San Francisco", etc. I'd do it across several industries, as well. I'd create a spreadsheet and notate the local pack ranking position of the top 3 and then its organic ranking. My bet will be that, at the end of the study, you'll find a high apparent correlation. It won't be the case for every single business appearing in the pack, because some will be there due to spam or other factors that have nothing to do with their website. But, my guess would be there would be a pretty high instance of those businesses with top 3 local rankings also having page 1-2 organic rankings.
For this search "Dentist Santa Fe", I see that the top 3 in the pack are all 1st page organically, and I see this phenomenon for many, many searches, and it offers a good explanation why an annual survey like Local Search Ranking Factors reflects that Local SEOs have noticed this behavior as being common.
I'm sorry I haven't seen a recent article on this, but doing a small study should be relatively easy if you should need to present proof of this phenomenon. Hope this helps, and if anyone in the community has authored or read such a study recently, please share!