Do what you need to do to accumulate more down payment money.

Such as them claiming that they sent money when they didn’t, or claiming they paid more than they really did, or them saying they owe less than they really do. 

With the interest rate you have and appreciation you are getting, you will make a ton of money in the long run. 

Think of home ownership without mortgage burdens as a way of making extra money through rent payments every month.

If it were me, I would try to buy out the current owner, and do a partnership with your money person.  

Put your money where your mouth is. 

I haven't seen much said about them but I'm satisfied with what I've experienced.. they've made me money and I collect rent every month.   

This can be particularly appealing if the seller is facing financial difficulties, needs to move quickly (perhaps due to relocation, divorce, or other personal issues), or the property has little to no equity and they can't afford to sell it through traditional means without bringing money to the closing.

The only people making money in NYC are the people that invested years ago or the people that are buying land and building the expensive condominiums on them.

Lots of money going to these sticky tenants, strong demand regardless of economy...