One doesn’t need to go to an R1 or R2 school to get research experience as an undergrad. Those designations are more important when you’re in grad school.
I would do a search on Columbia General Studies here in this forum and see what people’s experiences have been like.
College Navigator is a website done by the feds. It has a lot of information, including net price by income level and the number of graduates by field (for bachelor’s, master’s, doctoral). In the enrollment section it will indicate what percentage of students are age 25+.
This article I think might be really helpful for you. There’s a graph that sort of shows how the price for lower income families goes up as the chances of admission goes up. But there’s also a table near the bottom with the 100 schools with the lowest cost for families with $0-30k and $30-48k in income.
This list might be helpful for you in brainstorming possible colleges, but really, psychology is usually a bread & butter department, pretty strong at most schools.
This list shows which schools’ undergrads are producing the most PhDs in psychology. The list on the left is total by raw # (bigger schools are much better represented as they have had larger number of students) while the schools on the right have a higher # of grads when it’s evened out by the size of the institution. You’ll notice that attending an R1 or R2 institution for undergrad is by no means required.
With respect to your chances, your reaches are reaches for the most highly-qualified students. Going by transfer percentages, your chances might be better at USC or Cornell, but they would still be extremely challenging schools to get into.
Some reachier schools I’d look into are:
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College of William & Mary (VA): One of the country’s oldest colleges, and an excellent public institution. I knew that UVA met need for out-of-state students, but I learned today that William & Mary does, too.
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U. of Virginia
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Brandeis (MA)…but since 0% of their students are 25+, that might be a turnoff to you, and it might show where its institutional priorities are
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Tufts (MA)
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Trinity (TX)…it’s not the northeast, but it is very generous in determining financial need.
Also, I suspect that your odds would be pretty good for acceptance at Saint Peter’s in Jersey City (across from NYC). It’s a Jesuit school, and Jesuit schools tend to be very progressive. The Jesuit school near where I live has an active LGBTQ presence and supporters, and I’d be surprised if the same wasn’t true at other Jesuit schools across the country. Look and see how the NPC there compares to your in-state options.