One thing on your 100% need met. You need to run NPCs because what you think is your need is not necessarily what the college thinks is need. The CC is littered with stories of stunned students. There are now schools that promise x % of tuition based on income but again they look at assets as well. They always have a disclaimer. You can reach out to a 100% need school like U of Miami and get a zoom appointment for review, just to see. Washington & Lee will do this as well. This way you can measure your assumptions as you look at other schools.
I suggest applying to high merit schools whether Arizona, Alabama, MS State, Miami Ohio, etc They are good fallbacks in case your offer falls short of expectation. That is unless you are 100% certain up front.
As for the LGBTQ portion I’d look at each school. My son goes to Bama. Most say it’s an issue, very conservative. He says the students are accepting of everyone and the stereotypes are way overdone.
Good luck.