I just don't understand why this top 20 or nothing mentality. Even people with extremely strong profiles apply wider than that for a PhD. It's not unrealistic, but it's nearly impossible to tell the odds for only the top 20 (probably low for almost anyone). I don't know which rankings you are using, but there should be several amazing universities outside that range. And, although rankings do matter, they are usually far from being the best way to choose a program.
Assuming that you can get a great GRE score (shouldn't be too hard for someone with your profile), and the good letters of recommendation from your MSc, it looks to me like you should be able to get into an excellent program. But it's hard to tell if your school selection is just based on the top 20.