I was under the impression that most schools make an allowance for excluding a certain amount of home equity from the equation, in addition to excluding what’s in parents’ retirement accounts. You should fund the retirement and HSA accounts to the max now, for 2020 (I think this can sometimes be done if before April 15th) this year, in order to reduce your cash reserves, and also on January 1st of next year for 2022 - you may be able to hold off on submitting the FAFSA until January 2nd, 2022, for the regular admission schools. I think that if you don’t like the offers from the early action schools, you can refile the revised FAFSA with them with an appeal, too.
The biggest difference by far is going to be getting your cash reserves sheltered by buying a house. You would be better off purchasing a home by fall 2021, using the entire amount of your savings and mutual fund (if the mutual fund is not in a protected retirement fund). You can always take a HELOC on the house, if you need access to the money you put into the house, to pay tuition.
If your child is of a caliber to be thinking Penn or Smith, they’re probably going to get into SUNY schools, so you don’t need to limit your housing search to within the NYC limits, so that they’d qualify for CUNY.
BTW, if your child qualifies for CUNY schools, that must mean you are a NYC resident. In which case, with the cost of housing in NYC, 125K doesn’t seem like it leaves you that much room for tuition, living anywhere within commuting distance to jobs in NYC.