I had the same graphics issue in my 15” 2011 MacBook. After discovering that Linux ran fine on the machine I tried doing a fresh install using a patched version of Catalina from DOSDude1. To my surprise, it worked! If anyone else can get this method to work I’m very curious to know. I struggled to get this machine to do anything for weeks and I am just astonished that Catalina is running on it smoothly.