It's been a little while since you posted.... so hopefully you already got your sponsorship!
I just wanted to say that the sponsorship portion took the longest for me. They offered me the job (contingent on being able to get a visa) at the end of January. I didn't find out anything about sponsorship until March. After that part the rest was really fast, I think I had the VISA in hand about a week later. It may depend on how your sponsor does things.... mine hired out another company to deal with the VISA process.