Apologize in advance for a long post.
Financial Aid (FA) calculators only provide the most general answers; at Ivy schools individual situations can make similar figures result in big FA differences.
I'll focus on Princeton (S [g. 2014] was a recruited baseball player, D was a regular admit [g. 2017]), with some side info on Yale, Harvard, USC, Vandy, Duke, Miami, Penn, Dartmouth.
First, the basic information on P's FA really only applies to families with pure W-2 income and savings (bank, stock accounts). For the self-employed or benificiaries of a trust, the calculators don't work well.
Second, absolutely FA grants can be improved - especially for the self-employed by aggressive financial planning while S is in 10th grade (or earlier). We are self-employed and knew our business needed capital investment - the issue was when and over what period. We did it all while S was in 10th grade; that reduced our income considerably for the tax year used to calculate FA. (S received baseball offers from Yale, Harvard, and Princeton. Each came up with different numbers based on the same return. Yale came in at 9k, P at 32k, Harvard said they'd match anyone. Yale applied a cash flow analysis, while P seemed to stick more closely to the tax return. Ivy schools are permitted to adjust FA offers to match its peers.) BTW, both kids - while they overlapped - got identical FA. Once S graduated, and our earlier aggressive financial planning had run its course, we were full pay. Very, very painful for 2 years. Very, very nice for 4 years.
Moral here: plan well in advance; recognizing you will be squeezed like a lemon anyway.
Third, P increases FA if you are paying tuition for kids in private HS or college. (Also if you are paying for aged parents, health expenses or anything real but which doesn't directly appear on the FA app.)
Fourth, there is some degree of fudge when you are placing values on non-fungible assets - like real estate. For example, we own the building which housed our business. The value we used for our real estate assets was the price we could get in a quick sale (less the commission); this was considerably less then a Fair Market Value sale. Now, you can't lowball too much because Zillow will not support your number; but there is a pretty broad range and you should choose the low end of the range.
Fifth, I disagee strongly with the broad conclusion that a Princeton degree isnt worth the extra money. (If my kid was going to teach middle school, I agree. Moreover, if my kid was heading to medical school Id send him to a school where he could finish in the top 10% - because many grad schools base admissions on class rank and scores. Only the rarest player at P will do that.) My S - middle of the class econ major - working as a consultant (whatever that is) for an international firm gets paid more than his fellow consultants who finished top 10% - based solely on his school. My D - above middle Chem. Engineer with a finance "minor" - had no trouble getting multiple offers in Investment Banking; her work peers from great state flagships all finished near the top of their respective classes. So, for many careers not requiring graduate degrees, a Princeton degree has a great Return on Investment.
Sixth, my understanding is that families are expected to pay 5% on assets, salary, dividends over 300k. Primary residence and NORMAL retirement accumulations are exempt.
Turning to FA from other schools. No insult intended, but you need to drop down pretty far on the food chain to get huge discounts on college. D (the regular applicant) had 34 ACT, straight As in the most rigorous curriculum, 8 5s on AP tests, ran the HS division of the local food bank for 2 years, editor in chief of yearbook and literary journal for 2 years (both award winning), first place grand prize award winner of the Intel Science and Engineering fair, varsity athlete, and owner of her patent. She got NO academic money and NO FA offer from USC, Vandy, or Duke. Got 25k with a chance of full at Miami. Got NO FA offer from Dartmouth or Penn. She could have attended San Diego State for virtually nothing.
So, lets assume your S gets a 25k academic scholarship AND he's playing baseball (on another 25%). The athletic scholly carries with it the implied condition he contribute. If coach feels hes not carrying his weight it's gone (now, if hes in a conference with 4 year guarantees, he's gone from the team in an attempt to get him to transfer). The academic scholly requires certain benchmark grades. What happens to the kid who takes a legit hard major? Most likely drops his major to one where he can make grades. Not a good result for the next 40 years. (The kid in FA loses it if he flunks out or parents finances improve; nothing depends upon baseball or grades.)
For most kids, graduating Princeton is a golden ticket. Won't matter if a kid wants to work as a barista; matters alot if he wants to play baseball and become an analyst at JP Morgan. (My S's baseball class had guys going to JP, Bain, McKinsey, milb, Bank of America and med school [the true walkon]. No unemployed, no boomerangs.)
We're upper middle class with both parents undergrad from State U. We weren't going to pay for grad school and we weren't really hoping either would move home while they accumulated job experience or money. To us, Princeton fit those requirements. (Note what I dont say: imo, the education Princeton provided my kids isn't better then my alma matter gave me; but the opportunities, network, and peer students were better. If I had to do it all again, I'd do it in a minute.)
I can readily understand not wanting to reduce a family's life style and/or putting off retirement. There is no easy answer. (We tell our kids we spent some of our retirement on Princeton and when we run out a few years early, they take in their mother and set dad on an ice flow.)
PM me if you want to talk more.