Congratulations!!!

After waiver is done, you are free like a bird, you could fly everywhere. Your current situation is same as most people on this continent, that means, you can do as they do. You can work in company, you can apply for H1 or other status. Your idea for university H1 may be a good idea, which I do not know for sure. But I have an Indian colleague who first worked in our university with H1 then he went to a company. Then he h1 transfer. It means your idea is feasible, first get H1 in university, then go to company. good luck!