Hey Ed,
I'm not sure if you realize this, but you're never supposed to use aggregate Schema review markup on your homepage. More on this: https://whitespark.ca/blog/how-to-use-aggregate-review-schema-to-get-stars-in-the-serps/
So, skip that goal of stars showing up from this in relation to the homepage.
I want to be sure I'm understanding your goal here. I believe you're saying that you homepage isn't ranking for your core term. It's only ranking for branded searches. And this is making you think you need to make a landing page for your core term. If you only have one location, that really wouldn't be a best practice. Rather, you have to figure out what WILL move the needle for you and this core term (if anything). Some things (like proximity or filters) will be a brick wall you can't easily pass through. Others (like building authority) are what you're going to typically run into as recommended strategy. There is something about your competitors that is holding you lower than that coveted #1 spot, Ed, and a competitive audit is going to be the best solution to find out what that something is.
I did a post here on the Moz blog about doing a competitive audit to analyze local rankings, but you're talking about organic rank, right? That would be a bit different, though related. Either way, you've got to find that secret something. It could be proximity, it could be links, it could be content, it could be spam!
Am I understanding your topic correctly?