I agree that re-running the NPCs with your parents to make sure all the inputs are correct is the first step. There could be a mistake made with your figures, getting that re-checked is important.
Occidental and Davidson are both great schools. However, if your figures turn out to be correct - I don’t think either of them offer merit that would bring the cost down to $40k. I think the most Oxy offers is $30k/year in merit, which would leave almost $50K left to pay. You may have to give up the ‘dream’ of going to a very expensive school on one of the coasts. But luckily, there are still plenty of other schools that might work.
You are in a state with some really strong, affordable public options. I hope you have either Miami OH and/or The Ohio State University as schools you will apply to. They both offer great educations at a impressive price point for in-state students (even before likely merit awards if you have strong stats/scores). Don’t underestimate the value of graduating debt-free and having some money available during college that could be used to subsidize an unpaid internship, study abroad or summer experience. You would have a lot of flexibility in your decide to stay in-state and really figure out how to maximize the utility of the budget your parents have given you.
Good luck with whatever you decide, I think it is important to remember that you are the most important part of your educational experience. There are many many schools where you can get a great education in the areas you are interested in, and you can get the small school experience (through honors colleges, and other ways) even at large schools.
Edited to Add: Some schools that would probably come in at your price point as long as your stats/scores are strong:
Dickinson
Muhlenberg
Wooster
Denison
Beloit
Kalamazoo
Whittier College
University of the Pacific
There are many more out there, your areas of interest aren’t esoteric, and there are many many schools with good to excellent departments.