+1i don't think your stats will drag you down as much as your lack of substantive research for the "top twenty" in selectivity. It's true that a small minority get accepted to those schools due to phenomenal leadership or dedicated, stand-out humnanistic activity, so you'd have to judge if you think you have that. There are plenty of schools below the most selective that will give you consideration, and possibly even scholarship money to attend there. It will be a lot of work, money, and time off school attending interviews to take a shot at those other schools, and in the end only you, not your family, can decide if it's worth the effort.
You could also wait a year to apply and gain that additional research background if a name-brand school is really important enough.