Many american universities have programs where you can get your bachelors within 2 to 3 yrs, instead of 4. That makes you only 19 or 20 after you graduate
Maybe you can go to Al Azhar after that? Look for summer programs.
North America also has Al Maghrib Institute all over. I'm not exactly sure how it works, but they have seminars yearly and tests, too.
http://www.almaghrib.org/
I know exactly how you feel. You know that no matter what secular university you go to , it'll support your brain and break your heart into two. It doesn't make sense learn anything that doesn't involve Islam in it. Just once, you wish get taste the feeling to be in a learning environment of early Islam Baghdad.