You are well paid - rock on! Who cares though if you are or are not a "real" software engineer or not. You are clearly creating value in the world. Given that

You are well paid - rock on! Who cares though if you are or are not a "real" software engineer or not. You are clearly creating value in the world. Given that you've been working for the company for a while as a freelancer, I think the person hiring you has a pretty good idea of your relative productivity. It's certainly possible to be 5x more productive than your average developer - and schools have little to do with that. Good luck and have fun!