the funny thing is, how does not paying for college solve the gay thing? Are they thinking that you’re willing to make a sexuality switch in exchange for tuition? 
Yes, you can. Here are some that are automatic for your stats, according to http://automaticfulltuition.yolasite.com/ (however, some are first come first served, so apply early if interested):
Troy
Tuskegee
Alabama State
Arkansas - Monticello
Arkansas - Little Rock
Howard
Florida A&M
Louisiana Tech
North Carolina Central
Prairie View A&M
Competitive full rides are listed in this thread:
However, note that economics majors at various colleges can vary in math intensity. Chicago is more math intensive than most schools, which is preferable if you want to go on to PhD study (which also expects a much higher level of math and statistics preparation than typical economics major degree requirements).
One final bit of advice – I’d check http://www.campusprideindex.org/ if you are investigating schools that you may not have had on your original list. When we looked into several schools that we initially thought were perfect for my daughter we learned that they were very conservative and not at all LGBT friendly. It may not be of high importance to you, but for my daughter it was very important–she wants to feel comfortable with who she is and not have to pretend to be someone she’s not. She also didn’t want to be made fun of or called names and wants to have access to LGBT organizations and resources on campus. Several of the colleges she is applying to even have LGBT dorms.