OP, we already addressed your concern about animal shelters: They are kittens. That doesn't happen to healthy tame kittens. They WILL be adopted and you won't have to pay a thing for getting them fixed. The new owners will be vetted too. Win. Win. Win. That's what you do with strays. Probably should have done it while the mom was still preggers.
That isn't a safe assumption at all. It depends on the shelter. I worked in two different municipal shelters for about 3 years total. During the busy months aka "kitten season" I was tasked with euthanizing enough healthy tame kittens to fill a 45 gallon trash can, a couple of times each week. This was simply to make room for the kittens coming in each day, at the end of a long euthanasia day you would think we would have a couple empty cages, but no, there were never any empty cages. Frequently I would have to get the euthanasia drugs back out at closing time and stay late to make room for the last drop offs of the day.
Some might read the above and think it sounds cold blooded but it happens every day in every public shelter because of fucking fuckers who don't get their pets spayed and neutered.
There aren't enough homes for them all. OP, if you don't get them all fixed, or force adoptive owners to do so, you will be contributing to this problem.
Private no kill shelters exist, I'm on the BOD for one in my area. Some have intake fees, some don't. You're in a somewhat favorable position as "kitten season" hasn't yet reached full swing. It gets really bad around May and continues through autumn.
You can have an adoption contract that requires the new owner gets it done in X number of days. Feel free to include wording to the effect that if they fail to do so, MrColin will come to their house and damage the owners face. Alternatively, you can require them to pay up front, an amount that will cover the spay/neuter and they can pick up from the vet when they are ready.
Depending who you ask, one fertile female cat and its offspring can produce between 400 and 400,000 cats over seven years. I imagine in Brooklyn most of them would be squished in the road and/or eaten by sewer rats as kittens.
That girl and one of her kittens is a tortoiseshell, they are always pregnant in my experience. They are like the chubby redheads that get pregnant while on the pill and using condoms, extremely fertile.