You may want to look at the following lists of large merit scholarships:
http://automaticfulltuition.yolasite.com/
http://competitivefulltuition.yolasite.com/
http://nmfscholarships.yolasite.com/ (if National Merit)
You can then filter them by your criteria, including academic offerings and LGBT-friendliness, among other things. The automatic ones that you qualify for may be safeties, while the competitive ones would be match/reach for the scholarships (may be safety if you are certain to be admitted and you can afford them without the scholarships).