A top 50 MBA program will want work experience and that will be far more important than where you go.
It’s great to shoot high and you have no budget constraints. I was just noting if you get in nowhere - as I have no way to understand your profile so I don’t know if a GW or PSU are realistic or not.
If all fails, you’ll still have opportunities to get into other, less selective schools - although of course, you’d want to know why you didn’t get in somewhere - perhaps you haven’t met a minimum course requirement.
But there is definitely time to get into fine schools, that are simply less selective.
Hope you get into some on your first round.
Good luck.
Your parents, if they scraped together, can hold money back in savings. And the best education you can get is not necessarily at the most prestigious. Please don’t conflate “prestige” which is perceived vs. a quality education. They are not the same thing.
Good luck