I suggest pulling info from your local AHJ website for the Building Dep't. and harvesting names from that. Going back months, you should see some of the same names crop-up again and again.
You also need to recognize that you're dealing with a small job, so someone who is a big operation isn't going to be interested.
Contacting local architects for some referrals may give you some leads. The state licensing agency for GC's is a place to investigate complaints and resolutions. I wouldn't bother with the BBB. That's my belief, you can search for info from them on someone you're considering, and see how that compares to your other leads/sources.
Generally, the cities/counties aren't supposed to make any referrals, but having worked in development as an urban planner and plans examiner, in FL, I can go to people in the Building Dept's. I know, and get referrals. It's worked so-far for me, though I'm retired.
Looking at your state's division of corporations will help you to investigate the contractor's legal status to do business. You can usually search by corporate name, the registered agent, office-holders, fictitious names, and other ways. Someone who's businesses are changed every couple of years is probably not whom you want to entrust your project to. They're probably dodging lawsuits, and re-forming under a different corporate name to return to business. Here's an example of how it's organized in Florida:
https://dos.myflorida.com/sunbiz/search/