Limited Equity Coops

I'd contact all 80/20 buildings to get on their waitlists (tenant turnover subsequent to initial lottery). HPD and DHCR have lists ... you might need to go beyond their websites and contact bureaucrats by phone/email to get the lists.

Most buildings like Penn South are in the Mitchell-Lama coop programs. For those in desirable neighborhoods, they either have "open" waitlists (typically 17 years or so) or "closed", with periodic lotteries and then usually longish waits. For the latter, because of the lotteries, you can't even get on the waitlist unless you luck out.

There's a story in today's paper about infighting at Penn South over repairs, future status, etc.

You may want to look at HDFC co-ops. Many have income-restrictions, flip taxes, & may require all-cash purchases. But, those asking prices tend to be relatively low; as is the monthly maintenance.