Ok slightly confused here, you own your home outright but can not get a home equity loan against it? U of A is roughly 19 K a year to live there, so that is your base cost , if you got no aid you and your kid need to come up with 19K a year , they can borrow $5,500 their first year , it goes up slightly each year. So in this case you have to be able to pay roughly 14,000 each year. I doubt you will get FA but she should get some merit, which reduces the cost and public colleges tend to take more AP credits. If she decides to go to Georgia Tech for CS for example the out of state cost is roughly 45,000, she could still get the $5,500 gov loan but you would have to come up with 40K a year to offset the rest. Again I doubt you would get FA but merit is a possibility
You will more than likely not find a better deal than staying in state bc your instate flagship is pretty cheap, for example Rutgers in NJ is about 30K a years vs. 20 for U of A. The real factor here is 2 things can you afford to pay for her to go out of state either public or non public. ? She can not just take loans for 100% of the cost unless you are willing to take them for her. Second is how much merit scholarships she can get instate or out of state and you will not know that until the child applies and gets accepted. As mentioned run the NPC for some schools she is thinking about to get a rough idea.