It's a great post Jennifer. Independent dealer marketing is very different than franchise, but in some ways has advantages as well.
First, I recommend identifying what makes you special. What's your focus, what's your value. Are you aggressive with sub prime? Do you have low priced inventory? Do you specialize in low mileage, newer vehicles at fair prices?
Second, website. Most of the independent websites aren't great, which is why they cost 99 bucks a month. They aren't built for conversions, but that doesn't mean you can't get them. Trim the fat on the site, make it an easy experience for people to do what they want to do (look at inventory, apply for financing, value a trade).
Now, I'd start with paid social. Organic social is great, sounds like you have a handle on that, but paid social opens up a lot more doors. Targeting sub and near prime audiences on Facebook with ads promoting the ease of application and likelihood of approval, optimized for completed credit applications, can make a huge impact on sales. Running "automotive inventory ads" is a little trickier. Basically, everyone is running them...which means you and 50 other dealers are advertising to the same audience with the same carousel. It can drive cheap VDP views, but often not much else. Instead, look at running what are called "collection ads". This is still inventory driven, dynamic ads, but they also can use video and design to promote your value prop as a dealer.
Create events! (No, I don't mean buy one of the Facebook Events). OEM's have known for a long time that "Sign and Drive" and "Truck Month" type marketing creates a sense of urgency and activity. You don't answer to an OEM, so you can have "Truck Month" this month if you want. You can have a "Celebrate America" sale, promoting all your domestic made inventory. Year end liquidations, manager's specials, literally whatever you want to create and run.
People tend to forget that digital advertising is still advertising first, digital second.